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Research Article | Open Access

Certain subfamily of Bazilevič holomorphic functions involving the m-leaf polynomial

Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia; khmo.alshammari@uoh.edu.sa
Department of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514, Egypt; tms00@fayoum.edu.eg
Department of Mathematics, Adham University College, Umm AL-Qura University, Makkah, Saudi Arabia; akgadelrab@uqu.edu.sa
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Abstract

In this paper, we introduce and investigate a novel subfamily of Bazilevič functions, defined using the m-leaf polynomial and the principle of subordination. For this subfamily, we establish several properties, including subordination results, inclusion relationships, and sharp coefficient bounds. Furthermore, we derive a general Fekete–Szegö inequality, providing a solution to this classical problem for functions within the new subfamily.

Keywords

Holomorphic functionssubordinationBazilevičfunctionm-Leaf functionFekete–Szegöproblem
CLC number: 30C45

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AIMS Mathematics
Volume 11 Issue 6,
June 2026
Pages 15676-15690
DOI: 10.3934/math.2026644

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Cite this article:
Alshammari KMK, Seoudy TM, Amin AK. Certain subfamily of Bazilevič holomorphic functions involving the m-leaf polynomial. AIMS Mathematics, 2026, 11(6): 15676-15690. https://doi.org/10.3934/math.2026644

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Received: 18 February 2026
Revised: 16 May 2026
Accepted: 29 May 2026
Published: 15 June 2026
©2026 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)