Research article Special Issues

The impact of population aging on economic growth: a case study on China

  • Received: 10 January 2023 Revised: 20 February 2023 Accepted: 21 February 2023 Published: 01 March 2023
  • MSC : 62J05

  • The impact of population aging on economic growth is a very important issue in the process of population structure change. This paper first proposes research hypotheses based on a systematic literature review and theoretical analysis of the negative and positive effects of population aging on economic growth. Then, based on the data of 30 provinces in the Chinese Mainland from 2000 to 2019, this paper empirically tests the impact of population aging on economic growth and its impact mechanism using a static panel data model, a dynamic panel data model and a mediating effect model. Our empirical analysis leads to the following conclusions. First, population aging has a significant inhibitory effect on economic growth. Second, the industrial structure upgrading plays a mediating role in the process of population aging affecting economic growth; that is, population aging inhibits economic growth by affecting the overall upgrading of the industrial structure as well as the industrial rationalization and optimization. Last, some policy implications are proposed based on the research conclusions.

    Citation: Yue Liu, Liming Chen, Liangting Lv, Pierre Failler. The impact of population aging on economic growth: a case study on China[J]. AIMS Mathematics, 2023, 8(5): 10468-10485. doi: 10.3934/math.2023531

    Related Papers:

    [1] Ye Yue, Ghulam Farid, Ayșe Kübra Demirel, Waqas Nazeer, Yinghui Zhao . Hadamard and Fejér-Hadamard inequalities for generalized k-fractional integrals involving further extension of Mittag-Leffler function. AIMS Mathematics, 2022, 7(1): 681-703. doi: 10.3934/math.2022043
    [2] Khaled Matarneh, Suha B. Al-Shaikh, Mohammad Faisal Khan, Ahmad A. Abubaker, Javed Ali . Close-to-convexity and partial sums for normalized Le Roy-type q-Mittag-Leffler functions. AIMS Mathematics, 2025, 10(6): 14288-14313. doi: 10.3934/math.2025644
    [3] Xiuzhi Yang, G. Farid, Waqas Nazeer, Muhammad Yussouf, Yu-Ming Chu, Chunfa Dong . Fractional generalized Hadamard and Fejér-Hadamard inequalities for m-convex functions. AIMS Mathematics, 2020, 5(6): 6325-6340. doi: 10.3934/math.2020407
    [4] Ghulam Farid, Maja Andrić, Maryam Saddiqa, Josip Pečarić, Chahn Yong Jung . Refinement and corrigendum of bounds of fractional integral operators containing Mittag-Leffler functions. AIMS Mathematics, 2020, 5(6): 7332-7349. doi: 10.3934/math.2020469
    [5] Maryam Saddiqa, Ghulam Farid, Saleem Ullah, Chahn Yong Jung, Soo Hak Shim . On Bounds of fractional integral operators containing Mittag-Leffler functions for generalized exponentially convex functions. AIMS Mathematics, 2021, 6(6): 6454-6468. doi: 10.3934/math.2021379
    [6] Bushra Kanwal, Saqib Hussain, Thabet Abdeljawad . On certain inclusion relations of functions with bounded rotations associated with Mittag-Leffler functions. AIMS Mathematics, 2022, 7(5): 7866-7887. doi: 10.3934/math.2022440
    [7] Sabir Hussain, Rida Khaliq, Sobia Rafeeq, Azhar Ali, Jongsuk Ro . Some fractional integral inequalities involving extended Mittag-Leffler function with applications. AIMS Mathematics, 2024, 9(12): 35599-35625. doi: 10.3934/math.20241689
    [8] Gauhar Rahman, Iyad Suwan, Kottakkaran Sooppy Nisar, Thabet Abdeljawad, Muhammad Samraiz, Asad Ali . A basic study of a fractional integral operator with extended Mittag-Leffler kernel. AIMS Mathematics, 2021, 6(11): 12757-12770. doi: 10.3934/math.2021736
    [9] Hengxiao Qi, Muhammad Yussouf, Sajid Mehmood, Yu-Ming Chu, Ghulam Farid . Fractional integral versions of Hermite-Hadamard type inequality for generalized exponentially convexity. AIMS Mathematics, 2020, 5(6): 6030-6042. doi: 10.3934/math.2020386
    [10] Mohra Zayed, Maged G. Bin-Saad, Waleed K. Mohammed . On Mittag-Leffler-Gegenbauer polynomials arising by the convolution of Mittag-Leffler function and Hermite polynomials. AIMS Mathematics, 2025, 10(7): 16642-16663. doi: 10.3934/math.2025746
  • The impact of population aging on economic growth is a very important issue in the process of population structure change. This paper first proposes research hypotheses based on a systematic literature review and theoretical analysis of the negative and positive effects of population aging on economic growth. Then, based on the data of 30 provinces in the Chinese Mainland from 2000 to 2019, this paper empirically tests the impact of population aging on economic growth and its impact mechanism using a static panel data model, a dynamic panel data model and a mediating effect model. Our empirical analysis leads to the following conclusions. First, population aging has a significant inhibitory effect on economic growth. Second, the industrial structure upgrading plays a mediating role in the process of population aging affecting economic growth; that is, population aging inhibits economic growth by affecting the overall upgrading of the industrial structure as well as the industrial rationalization and optimization. Last, some policy implications are proposed based on the research conclusions.



    Geometric function theory is a fascinating branch of complex analysis that delves into the beautiful interplay between complex-valued functions and their geometric properties. It centers around understanding how these functions distort and transform shapes in the complex plane. Let ˜F(Ω) denote the space of all analytic functions in the open unit disk Ω={ϖC:|ϖ|<1} and let ˜F denote the class of functions ˜F(Ω) which has the form

    (ϖ)=ϖ+m=2amϖm. (1.1)

    Let ˜S denote the subclass of ˜F that includes all univalent functions within the domain Ω. The convolution, or Hadamard product, of two analytic functions and g, both of which belong to ˜F, is defined as follows: here, is given by (1.1), while the function g takes the form g(ϖ)=ϖ+m=2bmϖm, as

    (g)(ϖ)=ϖ+m=2ambmϖm.

    This research aims to define new starlike functions using the concepts of (u,v)-symmetrical functions and quantum calculus. Before delving into the discussion on (u,v)-symmetrical functions and quantum calculus (q-calculus), let us briefly review the essential concepts and symbols related to these theories.

    The theory of (u,v)-symmetrical functions is a specific area within geometric function theory that explores functions exhibiting a unique kind of symmetry. Regular symmetric functions treat all variables alike, but (u,v)-symmetrical functions introduce a twist. Here, v denotes a fixed positive integer, and u can range from 0 to v1, (see [1]). A domain ˜D is said to be v-fold symmetric if a rotation of ˜D about the origin through an angle 2πv carries ˜D onto itself. A function is said to be v-fold symmetric in ˜D if for every ϖ in ˜D and (e2πivϖ)=e2πiv(ϖ). A function is considered (u,v)-symmetrical if for any element ϖ˜D and a complex number ε with a special property (ε=e2πiv), the following holds:

    (εϖ)=εu(ϖ),

    where ε term introduces a rotation by a specific angle based on v, and the key concept is that applying this rotation to an element ϖ and then applying the function has the same effect as applying h to ϖ first and then rotating the result by a power of ε that depends on u. In our work we need the following decomposition theorem

    Lemma 1.1. [1] For every mapping :ΩC and a v-fold symmetric set Ω, there exists a unique sequence of (u,v)-symmetrical functions u,v, such that

    (ϖ)=v1u=0u,v(ϖ),u,v(ϖ)=1vv1n=0εnu(εnϖ),ϖΩ. (1.2)

    Remark 1.2. In other words, (1.2) can also be formulated as

    u,v(ϖ)=m=1δm,uamϖm,a1=1, (1.3)

    where

    δm,u=1vv1n=0ε(mu)n={1,m=lv+u;0,mlv+u;, (1.4)
    (lN,v=1,2,,u=0,1,2,,v1).

    The theory of (u,v)-symmetrical functions has many interesting applications; for instance, convolutions, fixed points and absolute value estimates. Overall, (u,v)-symmetrical functions are a specialized but powerful tool in geometric function theory. Their unique symmetry property allows researchers to delve deeper into the geometric behavior of functions and uncover fascinating connections. Denote be ˜F(u,v) for the family of all (u,v)-symmetric functions. Let us observe that the classes ˜F(1,2), ˜F(0,2) and ˜F(1,v) are well-known families of odd, even and of vsymmetrical functions, respectively.

    The interplay between q-calculus and geometric function theory is a fascinating emerging area of mathematical research The literature recognizes the fundamental characteristics of q-analogs, which have various applications in the exploration of quantum groups, q-deformed super-algebras, fractals, multi-fractal measures, and chaotic dynamical systems. Certain integral transforms within classical analysis have their counterparts in the realm of q-calculus. Consequently, many researchers in q-theory have endeavored to extend key results from classical analysis to their q-analogs counterparts. To facilitate understanding, this paper presents essential definitions and concept explanations of q-calculus that are utilized. Throughout the discussion, it is assumed that the parameter q adheres to the condition 0<q<1. Let's begin by reviewing the definitions of fractional q-calculus operators for a complex-valued function . In [2], Jackson introduced and explored the concept of the q-derivative operator q(ϖ) as follows:

    q(ϖ)={(ϖ)(qϖ)ϖ(1q),ϖ0,(0),ϖ=0. (1.5)

    Equivalently (1.5), may be written as

    q(ϖ)=1+m=2[m]qamϖm1ϖ0,

    where

    [m]q=1qm1q=1+q+q2+...+qm1. (1.6)

    Note that as q1, [m]qm. For a function (ϖ)=ϖm, we can note that

    q(ϖ)=q(ϖm)=1qm1qϖm1=[m]qϖm1.

    Then

    limq1q(ϖ)=limq1[m]qϖm1=mϖm1=(ϖ),

    where (ϖ) represents the standard derivative.

    The q-integral of a function was introduced by Jackson [3] and serves as a right inverse, defined as follows:

    ϖ0(ϖ)dqϖ=ϖ(1q)m=0qm(ϖqm),

    provided that the series m=0qm(ϖqm) converges. Ismail et al. [4] was the first to establish a connection between quantum calculus and geometric function theory by introducing a q-analog of starlike (and convex) functions. They generalized a well-known class of starlike functions, creating the class of q-starlike functions, denoted by Sq, which consists of functions ˜F that satisfy the inequality:

    |ϖ(q(ϖ))(ϖ)11q|11q,ϖΩ.

    Numerous subclasses of analytic functions have been investigated using the quantum calculus approach in recent years by various authors, like how Naeem et al. [5], explored subclesses of q-convex functions. Srivastava et al. [6] investigated subclasses of q-starlike functions. Govindaraj and Sivasubramanian in [7], identified subclasses connected with q-conic domain. Alsarari et al. [8,9]. examined the convolution conditions of q-Janowski symmetrical functions classes and studied (u,v)-symmetrical functions with q-calculus. Khan et al. [10] utilized the symmetric q-derivative operator. Srivastava [11] published a comprehensive review paper that serves as a valuable resource for researchers.

    The (u,v)-symmetrical functions are crucial for the exploration of various subclasses of ˜F. Recently, several authors have studied subclasses of analytic functions using the (u,v)-symmetrical functions approach, (see [12,13,14,15]). By incorporating the concept of the q-derivative into the framework of (u,v)-symmetrical functions, we will establish the following classes:

    Definition 1.3. Let q and α be arbitrary fixed numbers such that 0<q<1 and 0α<1. We define Sq(α,u,v) as the family of functions ˜F that satisfy the following condition:

    {ϖq(ϖ)u,v(ϖ)}>α,forallϖΩ, (1.7)

    where u,v is defined in (1.2).

    By selecting specific values for parameters, we can derive a variety of important subclasses that have been previously investigated by different researchers in their respective papers. Here, we enlist some of them:

    Sq(α,1,1) = Sq(α) which was introduced and examined by Agrawal and Sahoo in [16].

    Sq(0,1,1) = Sq which was initially introduced by Ismail et al. [4].

    S1(α,1,2) = S(α) the renowned class of starlike functions of order α established by Robertson [17].

    S1(0,1,1)=S the class introduced by Nevanlinna [18].

    S1(0,1,v) = S(0,k) the class introduced and studied by Sakaguchi [19].

    We denote by Tq(α,u,v) the subclass of ˜F that includes all functions for which the following holds:

    ϖq(ϖ)Sq(α,u,v). (1.8)

    We must revisit the neighborhood concept initially introduced by Goodman [20] and further developed by Ruscheweyh [21].

    Definition 1.4. For any ˜F, the ρ-neighborhood surrounding the function can be described as:

    Nρ()={g˜F:g(ϖ)=ϖ+m=2bmϖm,m=2m|ambm|ρ}. (1.9)

    For e(ϖ)=ϖ, we can see that

    Nρ(e)={g˜F:g(ϖ)=ϖ+m=2bmϖm,m=2m|bm|ρ}. (1.10)

    Ruschewegh [21] demonstrated, among other findings, that for all ηC, with |μ|<ρ,

    (ϖ)+ηϖ1+ηSNρ()S.

    Our main results can be proven by utilizing the following lemma.

    Lemma 1.5. [20] Let P(ϖ)=1+m=1pmϖm,(ϖΩ), with the condition {p(ϖ)}>0, then

    |pm|2,(m1).

    In this paper, our main focus is on analyzing coefficient estimates and exploring the convolution property within the context of the class Sq(α,u,v). Motivated by Definition 1.4, we introduce a new definition of neighborhood that is specific to this class. By investigating the related neighborhood result for Sq(α,u,v), we seek to offer a thorough understanding of the properties and characteristics of this particular class.

    We will now examine the coefficient inequalities for the function in Sq(α,u,u) and Tq(α,u,v).

    Theorem 2.1. If Sq(α,u,v), then

    |am|m1n=1(12α)δn,u+[n]q[n+1]qδn+1,u, (2.1)

    where δn,u is given by (1.4).

    Proof. The function p(ϖ) is defined by

    p(ϖ)=11α(ϖq(ϖ)u,v(ϖ)α)=1+m=1pmϖm,

    where p(ϖ) represents a Carathéodory function and (ϖ) belongs to the class Sq(α,u,v).

    Since

    ϖq(ϖ)=(u,v(ϖ))(α+(1α)p(ϖ)),

    we have

    m=2([m]qδm,u)amϖm=(ϖ+m=2amδm,uϖm)(1+(1α)m=1pmϖm),

    where δm,u is given by (1.4), δ1,u=1.

    By equating the coefficients of ϖm on both sides, we obtain

    am=(1α)([m]qδm,u)m1i=1δmi,uamipi,a1=1.

    By Lemma 1.5, we get

    |am|2(1α)|[m]qδm,u|.m1i=1δi,u|ai|,a1=1=δ1,u. (2.2)

    It now suffices to prove that

    2(1α)[m]qδm,u.m1n=1δm,u|au|m1n=1(12α)δn,u+[n]q[n+1]qδn+1,u. (2.3)

    To accomplish this, we utilize the method of induction.

    We can easily see that (2.3) is true for m=2 and 3.

    Let the hypotheses is be true for m=i.

    From (2.2), we have

    |ai|2(1α)[i]qδi,ui1n=1δn,u|an|,a1=1=δ1,u.

    From (2.1), we have

    |ai|i1n=1δn,u(12α)+[n]q[1+n]qδ1+n,u.

    By the induction hypothesis, we have

    (1α)2[i]qδi,ui1n=1δn,u|an|i1n=1(12α)δn,u+[n]q[1+n]qδ1+n,u.

    Multiplying both sides by

    (12α)δi,u+[i]q[1+i]qδ1+i,u,

    we have

    in=1(12α)δn,u+[n]q[n+1]qδn+1,u(12α)δi,u+[i]q[i+1]qδi+1,u[2(1α)[i]qδi,ui1n=1δn,u|an|]
    ={2(1α)δi,u[i]qδi,ui1n=1δn,u|an|+i1n=1δn,u|an|}.(1α)2[1+i]qδ1+i,u
    2(1α)[i+1]qδi+1,u{δi,u|ai|+i1n=1δn,u|an|}
    2(1α)[i+1]qδi+1,uin=1δn,u|an|.

    Hence

    (1α)2[1+i]qδ1+i,uin=1δn,u|an|in=1δn,u(12α)+[n]q[1+n]qδ1+n,u,

    This demonstrates that the inequality (2.3) holds for m=i+1, confirming the validity of the result.

    For q1,u=1 and v=1, we obtain the following well-known result (see [22]).

    Corollary 2.2. If S(α), then

    |ak|k1s=1(s2α)(k1)!.

    Theorem 2.3. If Tq(α,u,v), then

    |am|1[m]qm1n=1(12α)δn,u+[n]q[1+n]qδ1+n,u,form=2,3,4,..., (2.4)

    where δm,u is given by (1.4).

    Proof. By using Alexander's theorem

    (ϖ)Tq(α,u,v)ϖq(ϖ)Sq(α,u,v). (2.5)

    The proof follows by using Theorem 2.1.

    Theorem 2.4. A function Sq(α,u,v) if and only if

    1ϖ[{k(ϖ)(1eiϕ)+f(ϖ)(1+(12α)eiϕ)}]0, (2.6)

    where 0<q<1, 0α<1,0ϕ<2π and f,k are given by (2.10).

    Proof. Suppose that fSq(α,u,v), then

    11α(zϖq(ϖ)u,v(ϖ)α)=p(ϖ),

    if and only if

    ϖq(ϖ)u,v(ϖ)1+(12α)eiϕ1eiϕ. (2.7)

    For all ϖΩ and 0ϕ<2π, it is straightforward to see that the condition (2.7) can be expressed as

    1ϖ[ϖq(ϖ)(1eiϕ)u,v(ϖ)(1+(12α)eiϕ)]0. (2.8)

    On the other hand, it is well-known that

    u,v(ϖ)=(ϖ)f(ϖ),ϖq(ϖ)=(ϖ)k(ϖ), (2.9)

    where

    f(ϖ)=1vv1n=0ε(1u)nϖ1εnϖ=ϖ+m=2δm,uϖm,k(ϖ)=ϖ+m=2[m]qϖm. (2.10)

    Substituting (2.9) into (2.8) we get (2.6).

    Remark 2.5. From Theorem 2.4, it is straightforward to derive the equivalent condition for a function to be a member of the class Sq(α,u,v) if and only if

    (Tϕ)(ϖ)ϖ0,ϖΩ, (2.11)

    where Tϕ(ϖ) has the form

    Tϕ(ϖ)=ϖ+m=2tmϖm,tm=[m]qδm,u(δm,u(12α)+[m]q)eiϕ(α1)eiϕ. (2.12)

    In order to obtain neighborhood results similar to those found by Ruschewegh [21] for the classes, we define the following concepts related to neighborhoods.

    Definition 2.6. For any ˜F, the ρ-neighborhood associated with the function is defined as:

    Nβ,ρ()={g˜F:g(ϖ)=ϖ+m=2bmϖm,m=2βm|ambm|ρ},(ρ0). (2.13)

    For e(ϖ)=ϖ, we can see that

    Nβ,ρ(e)={g˜F:g(ϖ)=ϖ+m=2bmϖm,m=2βm|bm|ρ},(ρ0), (2.14)

    where [m]q is given by Eq (1.6).

    Remark 2.7.For βm=m, from Definition 2.6, we get Definition 1.4.

    For βm=[m]q, from Definition 2.6, we get the definition of neighborhood with q-derivative Nq,ρ(),Nq,ρ(e).

    For βm=|tm| given by (2.12), from Definition 2.6, we get the definition of neighborhood for the class Sq(α,u,v) with Nq,ρ(α,u,v;).

    Theorem 2.8. Let Nq,1(e), defined in the form (1.1), then

    |ϖq(ϖ)u,v(ϖ)1|<1, (2.15)

    where 0<q<1,ϖΩ.

    Proof. Let ˜F, and (ϖ)=ϖ+m=2amϖm,u,v(ϖ)=ϖ+m=2δm,uamϖm, where δm,u is given by (1.4).

    Consider

    |ϖq(ϖ)u,v(ϖ)|=|m=2([m]qδm,u)amϖm1|
    <|ϖ|m=2[m]q|am|m=2δm,u|am|.|ϖ|m1=|ϖ|m=2δm,u|am|.|ϖ|m1|u,v(ϖ)|,ϖΩ.

    This provides us with the desired result.

    Theorem 2.9. Let ˜F, and for any complex number η where |μ|<ρ, if

    (ϖ)+ηϖ1+ηSq(α,u,v), (2.16)

    then

    Nq,ρ(α,u,v;)Sq(α,u,v).

    Proof. Assume that a function g is defined as g(ϖ)=ϖ+m=2bmϖm and is a member of the class Nq,ρ(α,u,v;). To prove the theorem, we need to demonstrate that gSq(α,u,v). This will be shown in the following three steps.

    First, we observe that Theorem 2.4 and Remark 2.5 are equivalent to

    Sq(α,u,v)1ϖ[(Tϕ)(ϖ)]0,ϖΩ, (2.17)

    where Tϕ(ϖ)=ϖ+m=2tmϖm and tm is given by (2.12).

    Second, we find that (2.16) is equivalent to

    |(ϖ)Tϕ(ϖ)ϖ|ρ. (2.18)

    Since (ϖ)=ϖ+m=2amϖm˜F which satisfies (2.16), then (2.17) is equivalent to

    TϕSq(α,u,v)1ϖ[(ϖ)Tϕ(ϖ)1+η]0,|η|<ρ.

    Third, letting g(ϖ)=ϖ+m=2bmϖm we notice that

    |g(ϖ)Tϕ(ϖ)ϖ|=|(ϖ)Tϕ(ϖ)ϖ+(g(ϖ)(ϖ))Tϕ(ϖ)ϖ|
    ρ|(g(ϖ)(ϖ))Tϕ(ϖ)ϖ|(by using (2.18))
    =ρ|m=2(bmam)tmϖm|
    ρ|ϖ|m=2[m]qδm,u|[m]q+δm,u(12α)|1α|bmam|
    ρ|ϖ|ρ>0.

    This prove that

    g(ϖ)Tϕ(ϖ)ϖ0,ϖΩ.

    Based on our observations in (2.17), it follows that gSq(α,u,v). This concludes the proof of the theorem.

    When u=v=1, q1, and α=0 in the above theorem, we obtain (1.10), which was proven by Ruscheweyh in [21].

    Corollary 2.10. Let S represent the class of starlike functions. Let ˜F, and for all complex numbers η such that |μ|<ρ, if

    (ϖ)+ηϖ1+ηS, (2.19)

    then Nσ()S.

    In conclusion, this research paper successfully introduces and explores a novel category of q-starlike and q-convex functions, specifically Sq(α,u,v) and Tq(α,u,v), that are fundamentally linked to (u,v)-symmetrical functions. The findings highlight the intricate interplay between q-starlikeness, q-convexity, and symmetry conditions, offering a rich framework for further investigation. Through detailed analysis, including coefficient estimates and convolution conditions, this work lays a solid foundation for future studies in this area. The established properties within the (ρ,q)-neighborhood not only deepen our understanding of these function classes but also open avenues for potential applications in complex analysis and geometric function theory. Overall, this pioneering research marks a significant advancement in the study of special functions, inviting further exploration and development in this dynamic field.

    Hanen Louati conceptualized and led the development of the study's methodology, focusing on the formulation of new mathematical frameworks for q-starlike and q-convex functions. Afrah Al-Rezami contributed significantly to data validation and the theoretical exploration of (u,v)-symmetrical functions. Erhan Deniz conducted the primary analysis of coefficient inequalities and convolution properties, offering critical insights into the results. Abdulbasit Darem provided computational support and assisted in exploring the applications of the (ρ,q)-neighborhood framework. Robert Szasz contributed to the literature review, linking the study to prior research and assisting in the interpretation of findings. All authors participated in drafting the manuscript, revising it critically for important intellectual content. All authors have read and agreed to the published version of the manuscript.

    The authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA, for funding this research work through the project number "NBU-FPEJ-2024- 2920-02". This study was also supported via funding from Prince Sattam bin Abdulaziz University, project number (PSAU/2024/R/1445).

    All authors declare no conflicts of interest in this paper.



    [1] E. Kim, G. J. D. Hewings, C. Lee, Impact of educational investments on economic losses from population ageing using an interregional CGE-population model, Econ. Model., 54 (2016), 126–138. https://doi.org/10.1016/j.econmod.2015.12.015 doi: 10.1016/j.econmod.2015.12.015
    [2] F. Lancia, G. Prarolo, A politico-economic model of aging, technology adoption and growth, J. Popul. Econ., 25 (2012), 989–1018. https://doi.org/10.1007/s00148-011-0364-x doi: 10.1007/s00148-011-0364-x
    [3] Y. Su, Z. Li, C. Yang, Spatial interaction spillover effects between digital financial technology and urban ecological efficiency in China: an empirical study based on spatial simultaneous equations, Int. J. Environ. Res. Public Health, 18 (2021), 8535. https://doi.org/10.3390/ijerph18168535 doi: 10.3390/ijerph18168535
    [4] Y. Liu, P. Failler, Z. Liu, Impact of environmental regulations on energy efficiency: a case study of China's air pollution prevention and control action plan, Sustainability, 14 (2022), 3168. https://doi.org/10.3390/su14063168 doi: 10.3390/su14063168
    [5] Z. Li, G. Liao, K. Albitar, Does corporate environmental responsibility engagement affect firm value? The mediating role of corporate innovation, Bus. Strateg. Environ., 29 (2020), 1045–1055. https://doi.org/10.1002/bse.2416 doi: 10.1002/bse.2416
    [6] C. Y. Horioka, Aging and saving in Asia, Pac. Econ. Rev., 15 (2010), 46–55. https://doi.org/10.1111/j.1468-0106.2009.00489.x doi: 10.1111/j.1468-0106.2009.00489.x
    [7] Z. H. Li, J. H. Zhu, J. J. He, The effects of digital financial inclusion on innovation and entrepreneurship: a network perspective, Electron. Res. Arch., 30 (2022), 4697–4715. https://doi.org/10.3934/era.2022238 doi: 10.3934/era.2022238
    [8] M. B. Mimi, Md. Ahasan Ul Haque, Md. Golam Kibria, Does human capital investment influence unemployment rate in Bangladesh: a fresh analysis, National Accounting Review, 4 (2022), 273–286. https://doi.org/10.3934/NAR.2022016 doi: 10.3934/NAR.2022016
    [9] F. Sardo, Z. Serrasqueiro, Intellectual capital and high-tech firms' financing choices in the European context: a panel data analysis, Quant. Financ. Econ., 5 (2021), 1–18. https://doi.org/10.3934/QFE.2021001 doi: 10.3934/QFE.2021001
    [10] M. Gonzalez-Eiras, D. Niepelt, Ageing, government budgets, retirement, and growth, Eur. Econ. Rev., 56 (2012), 97–115. https://doi.org/10.1016/j.euroecorev.2011.05.007 doi: 10.1016/j.euroecorev.2011.05.007
    [11] J.-M. Le Page, Structural rate of unemployment, hysteresis, human capital, and macroeconomic data, National Accounting Review, 4 (2022), 135–146. https://doi.org/10.3934/NAR.2022008 doi: 10.3934/NAR.2022008
    [12] Y. Y. Huang, Q. Guo, M. X. Xiao, The unbalanced development and trends of China's regional tourism, National Accounting Review, 3 (2021), 69–85. https://doi.org/10.3934/NAR.2021003 doi: 10.3934/NAR.2021003
    [13] Z. Li, H. Chen, B. Mo, Can digital finance promote urban innovation? Evidence from China, Borsa Istanbul Rev., in press. https://doi.org/10.1016/j.bir.2022.10.006
    [14] Y. Liu, P. Failler, Y. Ding, Enterprise financialization and technological innovation: mechanism and heterogeneity, PLoS ONE, 17 (2022), e0275461. https://doi.org/10.1371/journal.pone.0275461 doi: 10.1371/journal.pone.0275461
    [15] L. Q. Zhao, Z. Y. Han, The research of economic development under the background of population aging in China, (Chinese), On Economic Problems, 2015, 40–44.
    [16] F. Gong, Z. Wang, J. Yu, Aging population, generational balance, and public welfare expenditure, Economic Research Journal, 54 (2019), 103–119.
    [17] M. Fougere, S. Harvey, J. Mercenier, M. Mérette, Population ageing, time allocation and human capital: a general equilibrium analysis for Canada, Econ. Model., 26 (2009), 30–39. https://doi.org/10.1016/j.econmod.2008.05.007 doi: 10.1016/j.econmod.2008.05.007
    [18] Z. Li, C. Yang, Z. Huang, How does the fintech sector react to signals from central bank digital currencies?, Financ. Res. Lett., 50 (2022), 103308. https://doi.org/10.1016/j.frl.2022.103308 doi: 10.1016/j.frl.2022.103308
    [19] S. Y. Ren, H. T. Wu, Path to green development: the role environmental regulation and labor skill premium on green total factor energy efficiency, Green Finance, 4 (2022), 387–410. https://doi.org/10.3934/GF.2022019 doi: 10.3934/GF.2022019
    [20] Y. Liu, Z. Li, M. Xu, The influential factors of financial cycle spillover: evidence from China, Emerg. Mark. Financ. Tr., 56 (2020), 1336–1350. https://doi.org/10.1080/1540496x.2019.1658076 doi: 10.1080/1540496x.2019.1658076
    [21] I. Semenenko, Y. Bilous, R. Halhash, The compliance of the regional development strategies and funding with the sustainable development concept: the case of Ukraine, Green Finance, 4 (2022), 159–178. https://doi.org/10.3934/GF.2022008 doi: 10.3934/GF.2022008
    [22] D. Qiu, D. J. Li, Comments on the "SSF Report" from the perspective of economic statistics, Green Finance, 3 (2021), 403–463. https://doi.org/10.3934/GF.2021020 doi: 10.3934/GF.2021020
    [23] G. K. Liao, P. Hou, X. Shen, K. Albitar, The impact of economic policy uncertainty on stock returns: the role of corporate environmental responsibility engagement, Int. J. Financ. Econ., 26 (2021), 4386–4392. https://doi.org/10.1002/ijfe.2020 doi: 10.1002/ijfe.2020
    [24] J. P. Ansah, R. L. Eberlein, S. R. Love, M. A. Bautista, J. P. Thompson, R. Malhotra, et al., Implications of long-term care capacity response policies for an aging population: a simulation analysis, Health Policy, 116 (2014), 105–113. https://doi.org/10.1016/j.healthpol.2014.01.006 doi: 10.1016/j.healthpol.2014.01.006
    [25] Y. Liu, C. Ma, Z. Huang, Can the digital economy improve green total factor productivity? An empirical study based on Chinese urban data, Math. Biosci. Eng., 20 (2023), 6866–6893. https://doi.org/10.3934/mbe.2023296 doi: 10.3934/mbe.2023296
    [26] M. Gonzalez-Eiras, D. Niepelt, Aging, government budgets, retirement, and growth, Eur. Econ. Rev., 56 (2011), 97–115. https://doi.org/10.1016/j.euroecorev.2011.05.007 doi: 10.1016/j.euroecorev.2011.05.007
    [27] K. Davis, The theory of change and response in modern demographic history, Population Index, 9 (1963), 345–352. https://doi.org/10.2307/2732014 doi: 10.2307/2732014
    [28] D. J. van de Kaa, The idea of a second demographic transition in industrialized countries, Sixth Welfare Policy Seminar of the National Institute of Population and Social Security, 29 January 2022, 1–34.
    [29] B. Siliverstovs, K. A. Kholodilin, U. Thiessen, Does aging influence structural change? Evidence from panel data, Econ. Syst., 35 (2011), 244–260. https://doi.org/10.1016/j.ecosys.2010.05.004 doi: 10.1016/j.ecosys.2010.05.004
    [30] M. Ahmed, M. Azam, S. Bekiros, S. M. Hina, Are output fluctuations transitory or permanent? New evidence from a novel Global Multi-scale Modeling approach, Quant. Financ. Econ., 5 (2021), 373–396. https://doi.org/10.3934/QFE.2021017 doi: 10.3934/QFE.2021017
    [31] P. Ilmakunnas, S. Ilmakunnas, Work force ageing and expanding service sector: a double burden on productivity?, Serv. Ind. J., 30 (2010), 2093–2110. https://doi.org/10.1080/02642060903199838 doi: 10.1080/02642060903199838
    [32] Z. Li, F. Zou, B. Mo, Does mandatory CSR disclosure affect enterprise total factor productivity?, Economic Research-Ekonomska Istraživanja, 35 (2022), 4902–4921. https://doi.org/10.1080/1331677X.2021.2019596 doi: 10.1080/1331677X.2021.2019596
    [33] Z. Li, Z. Huang, Y. Su, New media environment, environmental regulation and corporate green technology innovation: evidence from China, Energ. Econ., 119 (2023), 106545. https://doi.org/10.1016/j.eneco.2023.106545 doi: 10.1016/j.eneco.2023.106545
    [34] D. Qiu, D. Li, Paradox in deviation measure and trap in method improvement—take international comparison as an example, Quant. Financ. Econ., 5 (2021), 591–603. https://doi.org/10.3934/QFE.2021026 doi: 10.3934/QFE.2021026
    [35] Z. Wen, L. Chang, H. Tai, H. Liu, Testing and application of the mediating effects, Acta Psychologica Sinica, 36 (2004), 614–620.
    [36] X. Qu, L. Liu, Impact of environmental decentralization on high-quality economic development, (Chinese), Statistical Research, 38 (2021), 16–29. https://doi.org/10.19343/j.cnki.11-1302/c.2021.03.002 doi: 10.19343/j.cnki.11-1302/c.2021.03.002
    [37] M. Xu, Y. Jiang, Can the China's industrial structure upgrading narrow the gap between urban and rural consumption?, The Journal of Quantitative & Technical Economics, 32 (2015), 3–21.
    [38] C. Gan, R. Zheng, D. Yu, An empirical study on the effects of industrial structure on economic growth and fluctuations in China, Economic Research Journal, 46 (2011), 4–16.
    [39] Z. Li, Z. Huang, H. Dong, The influential factors on outward foreign direct investment: evidence from the "The Belt and Road", Emerg. Mark. Financ. Tr., 55 (2019), 3211–3226. https://doi.org/10.1080/1540496x.2019.1569512 doi: 10.1080/1540496x.2019.1569512
    [40] Z. Li, B. Mo, H. Nie, Time and frequency dynamic connectedness between cryptocurrencies and financial assets in China, Int. Rev. Econ. Financ., 2023, in press. https://doi.org/10.1016/j.iref.2023.01.015
  • This article has been cited by:

    1. H. M. Srivastava, Sarem H. Hadi, Maslina Darus, Some subclasses of p-valent γ
    -uniformly type q-starlike and q-convex functions defined by using a certain generalized q-Bernardi integral operator, 2023, 117, 1578-7303, 10.1007/s13398-022-01378-3
    2. Alina Alb Lupaş, Applications of the q-Sălăgean Differential Operator Involving Multivalent Functions, 2022, 11, 2075-1680, 512, 10.3390/axioms11100512
    3. Ali Mohammed Ramadhan, Najah Ali Jiben Al-Ziadi, New Class of Multivalent Functions with Negative Coefficients, 2022, 2581-8147, 271, 10.34198/ejms.10222.271288
    4. Sarem H. Hadi, Maslina Darus, Alina Alb Lupaş, A Class of Janowski-Type (p,q)-Convex Harmonic Functions Involving a Generalized q-Mittag–Leffler Function, 2023, 12, 2075-1680, 190, 10.3390/axioms12020190
    5. Abdullah Alatawi, Maslina Darus, Badriah Alamri, Applications of Gegenbauer Polynomials for Subfamilies of Bi-Univalent Functions Involving a Borel Distribution-Type Mittag-Leffler Function, 2023, 15, 2073-8994, 785, 10.3390/sym15040785
    6. Abdulmtalb Hussen, An application of the Mittag-Leffler-type Borel distribution and Gegenbauer polynomials on a certain subclass of bi-univalent functions, 2024, 10, 24058440, e31469, 10.1016/j.heliyon.2024.e31469
    7. Sarem H. Hadi, Maslina Darus, Firas Ghanim, Alina Alb Lupaş, Sandwich-Type Theorems for a Family of Non-Bazilevič Functions Involving a q-Analog Integral Operator, 2023, 11, 2227-7390, 2479, 10.3390/math11112479
    8. Sarem H. Hadi, Maslina Darus, Rabha W. Ibrahim, Third-order Hankel determinants for q -analogue analytic functions defined by a modified q -Bernardi integral operator , 2024, 47, 1607-3606, 2109, 10.2989/16073606.2024.2352873
    9. Haewon Byeon, Manivannan Balamurugan, T. Stalin, Vediyappan Govindan, Junaid Ahmad, Walid Emam, Some properties of subclass of multivalent functions associated with a generalized differential operator, 2024, 14, 2045-2322, 10.1038/s41598-024-58781-6
    10. Timilehin Gideon Shaba, Serkan Araci, Babatunde Olufemi Adebesin, 2023, Investigating q-Exponential Functions in the Context of Bi-Univalent Functions: Insights into the Fekctc-Szcgö Problem and Second Hankel Determinant, 979-8-3503-5883-4, 1, 10.1109/ICMEAS58693.2023.10429891
    11. Sarem H. Hadi, Maslina Darus, 2024, 3023, 0094-243X, 070002, 10.1063/5.0172085
    12. Sarem H. Hadi, Maslina Darus, Badriah Alamri, Şahsene Altınkaya, Abdullah Alatawi, On classes of ζ -uniformly q -analogue of analytic functions with some subordination results , 2024, 32, 2769-0911, 10.1080/27690911.2024.2312803
    13. Sarem H. Hadi, Khalid A. Challab, Ali Hasan Ali, Abdullah A. Alatawi, A ϱ-Weyl fractional operator of the extended S-type function in a complex domain, 2024, 13, 22150161, 103061, 10.1016/j.mex.2024.103061
    14. Ehsan Mejeed Hameed, Elaf Ali Hussein, Rafid Habib Buti, 2025, 3264, 0094-243X, 050109, 10.1063/5.0258939
    15. Girish D. Shelake, Sarika K. Nilapgol, Priyanka D. Jirage, 2025, 3283, 0094-243X, 040016, 10.1063/5.0265526
  • Reader Comments
  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(8527) PDF downloads(787) Cited by(20)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog