Coefficients and Fekete–Szegö Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials

Abdulmtalb Hussen () and Abdelbaset Zeyani
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Abdulmtalb Hussen: School of Engineering, Math, and Technology, Navajo Technical University, Lowerpoint Rd State Hwy 371, Crownpoint, NM 87313, USA
Abdelbaset Zeyani: Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260, USA

Mathematics, 2023, vol. 11, issue 13, 1-10

Abstract: Subclasses of analytic and bi-univalent functions have been extensively improved and utilized for estimating the Taylor–Maclaurin coefficients and the Fekete–Szegö functional. In this paper, we consider a certain subclass of normalized analytic and bi-univalent functions. These functions have inverses that possess a bi-univalent analytic continuation to an open unit disk and are associated with orthogonal polynomials; namely, Gegenbauer polynomials that satisfy subordination conditions on the open unit disk. We use this subclass to derive new approximations for the second and third Taylor–Maclaurin coefficients and the Fekete–Szegö functional. Furthermore, we discuss several new results that arise when we specialize the parameters used in our fundamental findings.

Keywords: Gegenbauer polynomials; bi-univalent functions; analytic functions; Taylor–Maclaurin coefficients; Fekete–Szegö functional (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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