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Research Article | Open Access

New subclass of generalized close-to-convex function relatedwith quasi-subordination

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

Keywords

close-to-convex functionquasi-convex functionquasi-subordinationintegral expressioncoefficient estimateFekete-Szegöproblem
CLC number: 30C45

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AIMS Mathematics
Volume 10 Issue 5,
May 2025
Pages 12149-12167
DOI: 10.3934/math.2025551

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Cite this article:
Aoen, Li S, Tula, et al. New subclass of generalized close-to-convex function relatedwith quasi-subordination. AIMS Mathematics, 2025, 10(5): 12149-12167. https://doi.org/10.3934/math.2025551

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Received: 07 February 2025
Revised: 21 April 2025
Accepted: 27 April 2025
Published: 15 May 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)