Bi-univalent Function Subclasses Subordinate to Horadam Polynomials

Abstract

The object of this article is to explore two subclasses of regular and bi-univalent functions subordinate to Horadam polynomials in the disk $\{\varsigma\in\mathbb{C}:|\varsigma| <1\}$. We originate upper bounds for the initial Taylor-Maclaurin coefficient estimates of functions in these subclasses. Fekete-Szeg\"o functional problem is also established. Furthermore, we present some new observations and investigate relevant connections to existing results.

Horadam Polynomials and a Class of Biunivalent Functions Defined by Ruscheweyh Operator

“…For more information about Horadam polynomials and its special interesting cases, we refer the readers to the articles [5,6,11,22,[25][26][27][28][29], the monograph [24], and the references therein.…”

“…However, Koebe function, 2z − z 2 /2 and z/1 − z 2 , does not belong to the class Σ. For more information about univalent and biunivalent functions, we refer the readers to the articles [4][5][6], the monographs [7][8][9], and the references therein.…”

“…In the year 1933, Fekete and Szegö [10] found the maximum value of |a 3 − λa 2 2 |, as a function of the real parameter 0 ≤ λ ≤ 1 for a univalent function f. Since then, the problem of dealing with the Fekete-Szegö functional for f ∈ A with any complex λ is known as the classical Fekete-Szegö problem. Tere are many researchers investigated the Fekete-Szegö functional and the other coefcient estimates problems, for example, see the articles [4][5][6][10][11][12][13][14][15][16][17][18][19][20] and the references therein.…”

A family of Analytic Functions Subordinate to Horadam Polynomials

“…For more information about Horadam polynomials and its special interesting cases, we refer the readers to the articles [1], [3], [2], [16], [18], [24], [26], [27], [30], the monograph [21], [29] and the references therein.…”

“…Since then, the problem of dealing with the Fekete-Szegö functional for f ∈ A with any complex λ is known as the classical Fekete-Szegö problem. There are many researchers investigated the Fekete-Szegö functional and the other coefficient estimates problems, for example see the articles [1], [5], [4], [6], [9], [13], [20], [22], [27], [30] and the references therein.…”