Initial Bounds for Certain Classes of Bi-Univalent Functions Defined by Horadam Polynomials

Abstract

The main purpose of this article is to make use of the Horadam polynomials hnx and the generating function Πx,z, in order to introduce three new subclasses of the bi-univalent function class σ. For functions belonging to the defined classes, we then derive coefficient inequalities and the Fekete–Szegö inequalities. Some interesting observations of the results presented here are also discussed. We also provide relevant connections of our results with those considered in earlier investigations.

Coefficient Bounds for a New Subclasses of Bi-Univalent Functions Associated with Horadam Polynomials

“…If we put in Theorem (1), we get the outcomes which were indicated by Alamoush [ 2 ]. In addition, if we put in Theorem (1), we get the outcomes which were indicated by Abirami et al [ 1 ]. In view of (36) and (37), equation 40becomes…”

“…Symbolized by the function class of the shape: The Koebe One-Quarter Theorem [ 4 ] shows that the image of includes a disk of radius ¼ under each function from . Thereby each univalent function of this kind has an inverse which fulfills The function is considered bi-univalent in if together and are univalent in Indicated by the Taylor-Maclaurin series expansion (1), the class of all bi-univalent functions in can be symbolized by . In the year 2010, Srivastava et al [ 10 ] refreshed the study of various classes of bi-univalent functions.…”

“…the class ( ) presented and investigated by Abirami et al[ 1 ]. Let the function indicated by (1) be in the class (…”

Coefficient Bounds and Fekete-Szegӧ Problem for a New Subclasses of Holomorphic Bi-Univalent Functions Defined by Horadam polynomials

“…1) For , the function class ℋ , , shortens to the function class , presented and investigated by Abirami et al [1].…”

Coefficient Bounds and Fekete-Szeg¨o inequality for a Certain Families of Bi-Prestarlike Functions Defined by (M,N)-Lucas Polynomials

“…A function U ∈ A is said to be bi-univalent in O if both U and U −1 are univalent in O, let we name by the notation E the set of bi-univalent functions in O satisfying (1.1). In fact, Srivastava et al [32] refreshed the study of holomorphic and biunivalent functions in recent years, it was followed by other works as those by Frasin and Aouf [15], Altinkaya and Yalçin Journal of Advances in Mathematics Vol 20 (2021) ISSN: 2347-1921 https://rajpub.com/index.php/jam [5], Güney et al [16] and others (see, for example [1,3,8,10,11,18,21,22,23,26,27,28,29,30,31,33,34,35,38,39,41]).…”