Loading [MathJax]/jax/output/SVG/jax.js
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] Miguel Vivas-Cortez, Muhammad Zakria Javed, Muhammad Uzair Awan, Artion Kashuri, Muhammad Aslam Noor . Generalized (p,q)-analogues of Dragomir-Agarwal's inequalities involving Raina's function and applications. AIMS Mathematics, 2022, 7(6): 11464-11486. doi: 10.3934/math.2022639
  • 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.



    In 1903, Mittag-Leffler [22] provided the function Eσ(z) defined by

    Eσ(z)=j=0 zjΓ(σj+1),(σ,zC,R(σ)>0),

    where Γ is the gamma function and R means the real part.

    Wiman [34] introduced the following generalized Mittag-Leffler function

    Eσ,μ(z)=j=0 zjΓ(σj+μ),(σ,μ,zC,[R(σ),R(μ)]>0).

    Prabhakar [25] introduced the following function Eρσ,μ(z) in the form

    Eρσ,μ(z)=j=0 (ρ)jΓ(μ+σj).zjj!,   (σ,μ,ρ,zC,[R(σ),R(μ),R(ρ)]>0).

    Later, Shukla and Prajapati [27] (see also [32]) defined another generalized Mittag-Leffler function

    Eρ,kσ,μ(z)=j=0 (ρ)kjΓ(μ+σj)zjj!,(σ,μ,ρ,zC,[R(σ),R(μ),R(ρ)]>0)

    where k(0,1)N and (ρ)kj=Γ(ρ+kj)Γ(ρ) is the generalized Pochhammer symbol defined as

    kkjkm=1(ρ+m1k)j if kN.

    Bansal and Prajapat [5] and Srivastava and Bansal [31] investigated geometric properties of the Mittag-Leffler function Eσ,μ(z), including starlikeness, convexity, and close-to-convexity (see [1,4,6,8,12,13,17,28,29]). In reality, the generalized Mittag-Leffler function Eσ,μ(z) and its extensions are still widely used in geometric function theory and in a variety of applications (see, for details, [2,3,7,16,24]).

    Let S(p) be the class of functions of the form

    f(z)=zp+j=p+1ajzj, (1.1)

    where f is holomorphic and multivalent in the open unit disk O={z:|z|<1}.

    Let f and F be two functions in S(p). Then the convolution (or Hadamard product), denoted by fF, is defined as

    (fF)(z)=zp+j=p+1ajdjzj=(Ff)(z),

    where f(z) is in (1.1) and F(z)=zp+j=p+1djzj.

    Let f(z) and h(z) be two analytic functions defined in O. The function f(z) is called subordinate to h(z), or h(z) is superordinate to f(z), denoted by f(z)h(z) and h(z)f(z), respectively, if there is a Schwarz function φ with φ(z)=0,|φ(z)|<1 and f(z)=h(φ(z)). If the function h is univalent in O, then the following equivalence is true if

    f(z)h(z)  (zO)f(0)=h(0) and f(O)h(O).

    Definition 1.1. ([18]). Let 0<q<1. Then [j]q! denotes the q-factorial, which is defined as follows:

    [j]q!={[j]q[j1]q[2]q[1]q,    j=1,2,3,1,    j=0

    where [j]q=1qj1q=1+j1m=1 qm and [0]q=0.

    Definition 1.2 ([18]). The q-generalized Pochhammer symbol [ρ]j,q, ρC, is given as

    [ρ]j,q=[ρ]q[ρ+1]q[ρ+2]q[ρ+j1]q,

    and the q-Gamma function is defined as

    Γq(ρ+1)=[ρ]qΓq(ρ) and Γq(1)=1.

    It follows that Γq(j+1)=[j]q!.

    Lately, many results have been given for some related special functions such as the Wright function [3] and multivalent functions (see [10,23,26]).

    Here, we propose a q-extension of specific extensions of the Mittag-Leffler function, motivated by the success of Mittag-Leffler function applications in physics, biology, engineering, and applied sciences. We generalize the Mittag-Leffler function given by Shukla and Prajapati [27] and obtain a new generalized q-Mittag-Leffler function.

    Now, we present a new generalized q-Mittag-Leffler function as follows

    Eρσ,μ(q;z)=z+j=2 (ρ)kjΓq(μ+σj)zjj!. (1.2)

    It is obvious that, when q1, the resulting function is the generalized Mittag-Leffler function, which is given by Shukla and Prajapati [27].

    Corresponding to the function Eρσ,μ(q;z) in (1.2), we establish the following generalized q-Mittag-Leffler function Eρσ,μ(p,q;z) in multivalent functions S(p), as given below

    Eρσ,μ(p,q;z)=zp+j=p+1 (ρ)k(jp)Γq(μ+σ(jp))zj(jp)!. (1.3)

    Again, using the new function (1.3), we define the following function:

    Gρσ,μ(p,q;z):=zpΓq(μ)Eρσ,μ(p,q;z)=zp+j=p+1 Γq(μ)(ρ)k(jp)Γq(μ+σ(jp))zj(jp)!. (1.4)

    Definition 1.3. For fS(p), we define the new linear operator Aμ,ρ;kσ;p,qf(z):S(p)S(p) by

    Aμ,ρ;kσ;p,qf(z)=Gρσ,μ(p,q;z)f(z)=zp+j=p+1 χjajzj, (1.5)

    where χj=Γq(μ)(ρ)kjΓq(μ+σj)j!.

    We now define a subclass Qμ,ρ;kσ;q(M,N;τ,p) of the family S(p) using the multivalent linear operator in (1.5) and the subordination concept.

    Definition 1.4. Let Aμ,ρ;kσ;p,qf(z) be an operator in (1.5). A function f(z)S(p) is said to be in the class Qμ,ρ;kσ;q(M,N;τ,p) if satisfies the following subordination condition:

    1pτ(z(Aμ,ρ;kσ;p,qf(z))Aμ,ρ;kσ;p,qf(z)τ)1+Mz1+Nz,  (zO) (1.6)

    or equivalently

    z(Aμ,ρ;kσ;p,qf(z))Aμ,ρ;kσ;p,qf(z)p+(pN+(MN)(pτ))z1+Nz,  (zO)

    and

    |z(Aμ,ρ;kσ;p,qf(z))Aμ,ρ;kσ;p,qf(z)pNz(Aμ,ρ;kσ;p,qf(z))Aμ,ρ;kσ;p,qf(z)[pN+(MN)(pτ)]|<1, (1.7)

    where 1M<N1, 0τ<p, and pN.

    Remark 1.1. Some well-known special classes of the class Qμ,ρ;kσ;q(M,N;τ,p) can be obtained by choosing the values of the parameters ς,μ,ρ;τ,k,p,q, M, and N.

    (1) Q0,0,10,1(M,N;τ,p)=Sp(M,N;τ,p) was provided by Aouf [2].

    (2) Q0,0,10,1(M,N;0,p)=Sp(M,N;p) was provided by Goel and Sohi [16].

    In this work, we introduce a new subclass of multivalent functions Qμ,ρ;kσ;q(M,N;τ,p) defined by the new linear operator Aμ,ρ;kσ;p,qf(z). And we study some geometric properties for the class Qμ,ρ;kσ;q(M,N;τ,p) such as the coefficient estimates, convexity and convex linear combination. Finally, the radius theorems associated with the generalized Srivastava-Attiya integral operator will be investigated.

    The first theorem in this section presents the necessary and sufficient condition for the function f(z) in (1.1) belong to the class Qμ,ρ;kσ;q(M,N;τ,p).

    Theorem 2.1. A function f(z) is in the class Qμ,ρ;kσ;q(M,N;τ,p) if and only if

    j=p+1 ((1+N)(jp)+(MN)(pτ))χj|aj|(MN)(pτ), (2.1)

    where 1M<N1, 0τ<p, and pN.

    Proof. Assume that the condition (2.1) is true. Then by (1.7), we have

    |z(Aμ,ρ;kσ;p,qf(z))pAμ,ρ;kσ;p,qf(z)||Nz(Aμ,ρ;kσ;p,qf(z))[(MN)(pτ)+pN]Aμ,ρ;kσ;p,qf(z)|=|j=p+1(jp)χjajzj||(MN)(pτ)zjj=p+1[Nj((MN)(pτ)+pN)]χjajzj|(MN)(pτ)+j=p+1[(1+N)(jp)+((MN)(pτ))]χj|aj|0.

    By maximum modulus theorem [11], we get f(z)Qμ,ρ;kσ;q(M,N;τ,p).

    Conversely, suppose that f(z)Qμ,ρ;kσ;q(M,N;τ,p). Then

    |z(Aμ,ρ;kσ;p,qf(z))Aμ,ρ;kσ;p,qf(z)pNz(Aμ,ρ;kσ;p,qf(z))Aμ,ρ;kσ;p,qf(z)[pN+(MN)(pτ)]|=|j=p+1(jp)χjajzj(MN)(pτ)zjj=p+1[Nj((MN)(pτ)+pN)]χjajzj|<1.

    Since R(z)|z|, we get

    R{j=p+1(jp)χjajzj(MN)(pτ)zjj=p+1[Nj((MN)(pτ)+pN)]χjajzj}<1.

    Taking z1, we have

    j=p+1 ((1+N)(jp)+(MN)(pτ))χj|aj|(MN)(pτ).

    This completes the proof.

    Theorem 2.2. Let f1 and f2 be analytic functions in the class Qμ,ρ;kσ;q(M,N;τ,p). Then f1f2Qμ,ρ;kσ;q(M,N;τ,p), where

    τ1=p(1p)(1+N)(MN)(pτ)2χ1[((1+N)(1p)+(MN)(pτ1))χ1]2(MN)2(pτ)2χ1, (2.2)

    where χ1=Γq(μ)(ρ)kΓq(μ+ς).

    Proof. We will show that τ1 is the largest satisfying

    j=p+1 ((1+N)(jp)+(MN)(pτ1))χj(MN)(pτ1)aj,1aj,21. (2.3)

    Since f1,f2Qμ,ρ;kσ;q(M,N;τ,p), by the condition (2.1) and the Cauchy-Schwarz inequality, we get

    j=p+1 ((1+N)(jp)+(MN)(pτ))χj(MN)(pτ)aj,1aj,21. (2.4)

    From (2.3) and (2.4), we observe that

    aj,1aj,2[((1+N)(jp)+(MN)(pτ))χj](pτ1)[((1+N)(jp)+(MN)(pτ1))χj](pτ).

    From (2.4), it is necessary to prove

    (MN)(pτ)((1+N)(jp)+(MN)(pτ))χj[((1+N)(jp)+(MN)(pτ))χj](pτ1)[((1+N)(jp)+(MN)(pτ1))χj](pτ). (2.5)

    Furthermore, from the inequality (2.5) it follows that

    τ1p(jp)(1+N)(MN)(pτ)2χj[((1+N)(jp)+(MN)(pτ1))χj]2(MN)2(pτ)2χj.

    Now, set

    E(j)=p(jp)(1+N)(MN)(pτ)2χj[((1+N)(jp)+(MN)(pτ1))χj]2(MN)2(pτ)2χj.

    We observe that the function E(j) is increasing for jN. Putting j=1, we have

    τ1=E(1)=p(1p)(1+N)(MN)(pτ)2χ1[((1+N)(1p)+(MN)(pτ1))χ1]2(MN)2(pτ)2χ1.

    This completes the proof.

    Theorem 2.3. Let f1 and f2 be analytic functions in the class Qμ,ρ;kσ;q(M,N;τ,p) of forms given in (1.1) with aj,1 and aj,2, respectively. Then

    w(z)=zp+j=p+1(a2j,1+a2j,2)zjQμ,ρ;kσ;q(M,N;τ,p),

    where

    η=p(1p)(1+N)(MN)(pτ)2χ1[((1+N)(1p)+(MN)(pτ1))χ1]2(MN)2(pτ)2χ1.

    Proof. By Theorem 2.1, we have

    j=p+1 [((1+N)(jp)+(MN)(pτ))χj(MN)(pτ)]2a2j,sj=p+1 [((1+N)(jp)+(MN)(pτ))χj(MN)(pτ)aj,s]21, (s=1,2).

    From the above inequality, we obtain

    j=p+1 12[((1+N)(jp)+(MN)(pτ))χj(MN)(pτ)]2(a2j,1+a2j,2)1.

    Therefore, the largest η can be obtained such that

    ((1+N)(jp)+(MN)(pτ))χj(MN)(pτ)12[((1+N)(jp)+(MN)(pτ))χj(MN)(pτ)]2.

    That is,

    ηp2(jp)(1+N)(MN)(pτ)2χ1[((1+N)(jp)+(MN)(pτ1))χ1]22(MN)2(pτ)2χ1.

    Now, set

    E(j)=p2(jp)(1+N)(MN)(pτ)2χ1[((1+N)(jp)+(MN)(pτ1))χ1]22(MN)2(pτ)2χ1.

    We observe that the function E(j) is increasing for jN. Putting j=1, we have

    η=E(1)=p2(1p)(1+N)(MN)(pτ)2χ1[((1+N)(1p)+(MN)(pτ1))χ1]22(MN)2(pτ)2χ1.

    This completes the proof.

    Theorem 2.4. Let f1,f2Qμ,ρ;kσ;q(M,N;τ,p). Then for γ[0,1], the function F(z)=(1γ)f1+γf2 belongs to the class Qμ,ρ;kσ;q(M,N;τ,p).

    Proof. Since the functions f1 and f2 belong to the class Qμ,ρ;kσ;q(M,N;τ,p),

    F(z)=(1γ)f1+γf2=zp+j=p+1ηjzj,

    where ηj=(1γ)aj,1+γaj,2.

    By (2.1), we observe that

    j=p+1 ((1+N)(jp)+(MN)(pτ))χj[(1γ)aj,1+γaj,2]=(1γ)j=p+1 ((1+N)(jp)+(MN)(pτ))χjaj,1+γj=p+1 ((1+N)(jp)+(MN)(pτ))χjaj,2(1γ)(MN)(pτ)+γ(MN)(pτ).

    Hence F(z)Qμ,ρ;kσ;q(M,N;τ,p).

    Theorem 2.5. Let fs(z)=zp+j=p+1aj,szj be in the class Qμ,ρ;kσ;q(M,N;τ,p) for s=1,2,,m. Then the function P(z)=ms=1sfs, where ms=1s=1, is also in the class Qμ,ρ;kσ;q(M,N;τ,p).

    Proof. By Theorem 2.1, we have

    j=p+1 ((1+N)(jp)+(MN)(pτ))χj(MN)(pτ)aj,s1.

    Since

    P(z)=ms=1sfs=ms=1s(zp+j=p+1aj,szj)=zp+j=p+1(ms=1saj,s)zj,
    j=p+1((1+N)(jp)+(MN)(pτ))χj(MN)(pτ)ms=1saj,s1.

    Thus P(z)Qμ,ρ;kσ;q(M,N;τ,p).

    In this section, we investigate radii of multivalent starlikeness, multivalent convexity, and multivalent close-to-convex for the function f(z) in the class Qμ,ρ;kσ;q(M,N;τ,p) with the generalized integral operator of Srivastava-Attiya.

    Jung et al. [19] introduced an integral operator with one parameter as follows:

    Iδ(f)(z):=2δzΓ(δ)z0 (log(zv) )δ1f(v)dv=z+j=2 (2j+1)δajzj(δ>0;fS).

    In 2007, Srivastava and Attiya [30] investigated a new integral operator, which is called Srivastava-Attiya operator, given by

    Ju,mf(z)=z+j=1(1+uj+u)δajzj.

    Many studies are concerned with the study of the operator of Srivastava-Attiya (see [9,14,15,20]).

    Mishra and Gochhayat [21] (also [33]) provided a fractional differintegral operator Jmu,pf(z):S(p)S(p) which is called a generalized of Srivastava-Attiya integral operator, defined by

    Jmu,pf(z)=zp+j=p+1(p+uj+u)δajzj. (3.1)

    Theorem 3.1. If f(z)Qμ,ρ;kσ;q(M,N;τ,p) and 0τ<p, then Jmu,pf(z) in (3.1) is multivalent starlike of order τ in |z|r1, where

    r1=infjp+1{((1+N)(jp)+(MN)(pτ))χj(j+u)δ(MN)(j2p+τ)(p+u)δ}. (3.2)

    Proof. According to the definition of a starlike function in [28], we have

    |z(Jmu,pf(z))Jmu,pf(z)p|pτ, (3.3)
    |z(Jmu,pf(z))Jmu,pf(z)p|=|j=p+1(jp)(p+uj+u)δajzjj=p+1(p+uj+u)δajzj|j=p+1(jp)(p+uj+u)δaj|z|jj=p+1(p+uj+u)δaj|z|j.

    By (3.2), we have

    j=p+1(j2p+τ)(p+u)δaj|z|j(pτ)(j+u)δ1.

    By (2.1) in Theorem 2.1, it is clear that

    (j2p+τ)(p+u)δ(pτ)(j+u)δ|z|j((1+N)(jp)+(MN)(pτ))χj(MN)(pτ).

    Therefore,

    |z|{((1+N)(jp)+(MN)(pτ))χj(j+u)δ(MN)(j2p+τ)(p+u)δ}1j.

    This completes the proof.

    Theorem 3.2. If f(z)Qμ,ρ;kσ;q(M,N;τ,p) and 0τ<p, then Jmu,pf(z) in (3.1) is multivalent convex of order τ in |z|r2, where

    r2=infjp+1{((1+N)(jp)+(MN)(pτ))χjp(j+u)δ(MN)[j(j2p+τ)](p+u)δ}. (3.4)

    Proof. To verify (3.4), it is necessary to prove

    |(1+z(Jmu,pf(z))(Jmu,pf(z)))p|pτ,

    but the result is obtained by repeating the steps in Theorem 3.1.

    Corollary 3.1. If f(z)Qμ,ρ;kσ;q(M,N;τ,p) and 0τ<p, then Jmu,pf(z) in (3.1) is multivalent close-to-convex of order τ in |z|r3, where

    r3=infj1{((1+N)(jp)+(MN)(pτ))χj(j+u)δ(MN)j(p+u)δ}. (3.5)

    In this work, we established and investigated a new generalized Mittag-Leffler function, which is a generalization of q-Mittag-Leffler function defined by Shukla and Prajapati [27]. Also, we studied some of the geometric properties of a certain subclass of multivalent functions. In addition, we introduced radius theorem using a generalized Srivastava-Attiya integral operator. Since the Mittag-Leffler function is of importance, it is related to a wide range of problems in mathematical physics, engineering, and the applied sciences. The results obtained in this article may have many other applications in special functions.

    The authors express many thanks to the Editor-in-Chief, handling editor, and the reviewers for their outstanding comments that improve our paper.

    The authors declare that they have no competing interests concerning the publication of this article.



    [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(8282) PDF downloads(776) Cited by(19)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog