New subclass of generalized close-to-convex function related	with quasi-subordination

Aoen; Shuhai Li; Tula; Shuwen Li; Hang Gao; Aoen; Shuhai Li; Tula; Shuwen Li; Hang Gao

doi:10.3934/math.2025551

AIMS Mathematics

2025, Volume 10, Issue 5: 12149-12167. doi: 10.3934/math.2025551

Previous Article Next Article

Research article Topical Sections

New subclass of generalized close-to-convex function related with quasi-subordination

Aoen ^{1,2
,},
Shuhai Li ^{2
,},
Tula ^{3
,},
Shuwen Li ^{1
,
,},
Hang Gao ^{1
,}

1.
College of Mathematics and Statistics, Northeast Normal University, Jilin 130024, China; cfxyaoen@sina.com, lisw739@nenu.edu.cn, hangg@nenu.edu.cn
2.
College of Mathematics and Computer Science, Chifeng University, Inner Mongolia 024000, China; cfxyaoen@sina.com, lishms66@163.com
3.
College of Continuing Education, Chifeng University, Inner Mongolia 024000, China; 248390750@qq.com

Received: 07 February 2025 Revised: 21 April 2025 Accepted: 27 April 2025 Published: 27 May 2025
MSC : 30C45

In this paper, we introduce a new class of generalized close-to-convex functions, which are defined by quasi-subordination relationship. The integral expression, the estimation of the first two terms and the Fekete-Szegö problem of functions belonging to the class are obtained. Our results extend and unify previous work on starlike, convex, and close-to-convex functions under quasi-subordination. Examples are provided to demonstrate sharpness.
- close-to-convex function,
- quasi-convex function,
- quasi-subordination,
- integral expression,
- coefficient estimate,
- Fekete-Szegöproblem
Citation: Aoen, Shuhai Li, Tula, Shuwen Li, Hang Gao. New subclass of generalized close-to-convex function relatedwith quasi-subordination[J]. AIMS Mathematics, 2025, 10(5): 12149-12167. doi: 10.3934/math.2025551

Related Papers:

Abstract

In this paper, we introduce a new class of generalized close-to-convex functions, which are defined by quasi-subordination relationship. The integral expression, the estimation of the first two terms and the Fekete-Szegö problem of functions belonging to the class are obtained. Our results extend and unify previous work on starlike, convex, and close-to-convex functions under quasi-subordination. Examples are provided to demonstrate sharpness.

References

[1]	R. S. Robertson, Quasi-subordination and coefficient conjectures, Bull. Amer. Math. Soc., 620 (1970), 1–9.
[2]	S. Y. Lee, Quasi-subordinate functions and coefficient conjectures, J. Korean Math. Soc., 12 (1975), 43–50.
[3]	F. Y. Ren, S. Owa, S. Fukui, Some inequalities on quasi-subordinate functions, Bull. Austr. Math. Soc., 43 (1991), 317–324. https://doi.org/10.1017/S0004972700029117 doi: 10.1017/S0004972700029117
[4]	O. Altmtas, S. Owa, Majorizations and quasi-subordinations for certain analytic functions, Proc. Jpn. Acad. Ser. A Math. Sci., 68 (1992), 181–85. https://doi.org/10.3792/pjaa.68.181 doi: 10.3792/pjaa.68.181
[5]	M. M. Mohd, M. Darus, Fekete-Szegö problems for quasi-subordination classes, J. Abstr. Appl. Anal., 3 (2012), 1–14. https://doi.org/10.1155/2012/192956 doi: 10.1155/2012/192956
[6]	P. Gurusamy, J. Sokoł, S. Sivasubramanian, The Fekete-Szegö functional associated with $k$-th root transformation using quasi-subordination, C. R. Math., 353 (2015), 617–622. https://doi.org/10.1016/j.crma.2015.03.016 doi: 10.1016/j.crma.2015.03.016
[7]	R. El-Ashwah, S. Kanas, Fekete-Szegö inequalities for quasi-subordination functions classes of complex order, Kyungpook Math.J., 55 (2015), 679–688. https://doi.org/10.5666/KMJ.2015.55.3.679 doi: 10.5666/KMJ.2015.55.3.679
[8]	C. Ramachandran, T. Soupramanien, J. Sokoł, The Fekete-Szegö functional associated with $k$-th root transformation using quasi-subordination, J. Math., 28 (2020), 199–208. DOI:10.1007/s41478-017-0059-0 doi: 10.1007/s41478-017-0059-0
[9]	P. P. Vyas, S. Kant, Certain subclasses of bi-univalent functions associated with quasi-subordination, J. Rajasthan Acad. Phys. Sci., 15 (2016), 315–325. https://www.researchgate.net/publication/315831303
[10]	Ş. Altinkaya, S. Yalçin, Quasi-subordinations for certain subclasses of bi-univalent functions, Math. Adv. Pure Appl. Sci., 1 (2018), 56–64.
[11]	S. P. Goyal, O. Singh, R. Mukherjee, Certain results on a subclass of analytic and bi-univalent functions associated with coefficient estimates and quasi-subordination, Palest. J. Math., 5 (2016), 79–85.
[12]	J. H. Choi, New subclass of bi-univalent functions based on quasi-subordination, Int. J. Appl. Math., 36 (2023), 685–697. https://doi.org/10.12732/ijam.v36i5.8 doi: 10.12732/ijam.v36i5.8
[13]	S. G. A. Shah, S. Hussain, A. Rasheed, Z. Shareef, Application of quasi-subordiantion to certain classes of meromorphic fucntions, J. Funct. Spaces, 2020 (2020), 4581926. https://doi.org/10.1155/2020/4581926 doi: 10.1155/2020/4581926
[14]	Aoen, L. Shuhai, H. Tang, Siqinqimuge, Some properties of certain subclasses of p-valent meromorphic functions associated with quasi-subordination, J. Math. Res. Appl., 38 (2018), 147–161. DOI:10.3770/j.issn:2095-2651.2018.02.005 doi: 10.3770/j.issn:2095-2651.2018.02.005
[15]	K. R. Karthikeyan, G. Murugusundaramoorthy, N. E. Cho, Some inequalities on Bazilevi$\check{c}$ class of functions involving quasi-subordination, AIMS Math., 6 (2021), 7111–7124. https://doi.org/10.3934/math.2021417 doi: 10.3934/math.2021417
[16]	S. G. A. Shah, S. Al-Sa'di, S. Hussain, A. Tasleem, A. Rasheed, I. Z. Cheema, et al., Fekete-Szegö functional for a class of non-Bazilevi$\check{c}$ functions related to quasi-subordination, Demonstr. Math., 56 (2023), 1–10. https://doi.org/10.1515/dema-2022-0232 doi: 10.1515/dema-2022-0232
[17]	M. Çağlar, P. Gurusamy, H. Orhan, The coefficient estimates for a class defined by hohlov operator using conic domains, Twms J. Pure Appl., 11 (2020), 157–172.
[18]	K. Y. Taha, S. A. Rahman, Juma, Fekete-Szegö problem for certain subclass of q-difference operator using quasi-subordination, Tikrit J. Pure Sci., 26 (2021), 91–94. https://doi.org/10.25130/tjps.v26i6.197 doi: 10.25130/tjps.v26i6.197
[19]	Aoen, L. Shuhai, T. Huo, Coefficient related problem studies for new subclass of bi-univalent functions defined by $(s, t)$-derivative operator and quasi-subordination, J. Math. Res. Appl., 41 (2021), 579–593. DOI:10.3770/j.issn:2095-2651.2021.06.003 doi: 10.3770/j.issn:2095-2651.2021.06.003
[20]	S. Gurmeet, S. Gurcharanjit, S. Gagandeep, Certain subclasses of bi-close-to-convex functions associated with quasi-subordination, Abstr. Appl. Anal., 2019 (2019), 6947020. https://doi.org/10.1155/2019/6947020 doi: 10.1155/2019/6947020
[21]	Aoen, L. Shuhai, Some properties of generalized complex-order $\alpha$ type Bazilevi$\check{c}$ functions, J. Yangzhou Univer., 26 (2023), 42. DOI:10.19411/j.1007-824x.2023.03.001 doi: 10.19411/j.1007-824x.2023.03.001
[22]	H. Arikan, H. Arikan, H. Orhan, Fekete-Szeg$\ddot{o}$ problem for subclasses of analytic functions associated with quasi-subordination, Bulletin of the Transilvania University of Braşov Series Ⅲ: Mathematics, Informatics, Physics, 61 (2019), 221–232. https://doi.org/10.31926/but.mif.2019.12.61.2.3
[23]	M. J. Marut, M. H. Mohd, S. Supramaniam, The Fekete-Szegö inequalities for meromorphic functions associated with quasi-subordination, AlP Conf. Proc., 2184 (2019), 020005. https://doi.org/10.1063/1.5136359 doi: 10.1063/1.5136359
[24]	Aoen, L. Shuhai, T. Huo, Coefficient estimates and Fekete-Szegö inequality for new subclass of bi-Bazilevi$\check{c}$ functions by $(s, t)$-derivative operator and quasi-subordination, J. Math. Inequal., 15 (2021), 923–940. https://dx.doi.org/10.7153/jmi-2021-15-64 doi: 10.7153/jmi-2021-15-64
[25]	l. A. R. Ahman, W. G. Atshan, Results on coefficients bounds for new subclasses by using quasi-subordination of analytic function estimates, AlP Conf. Proc., 2398 (2022), 060021. https://doi.org/10.1063/5.0093380 doi: 10.1063/5.0093380
[26]	P. L. Duren, Univalent functions, Springer-Verlag, 1983.
[27]	S. Srikandan, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20 (1969), 8–12. https://doi.org/10.20935/MHealthWellB7426 doi: 10.20935/MHealthWellB7426
[28]	Z. Nehari, Conformal mapping, Courier Corporation, 1975.

Reader Comments

Your name:*

Email:*
© 2025 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)