Fekete-Szegö inequality for analytic and bi-univalent functions subordinate to Chebyshev polynomials

Abstract

In the present paper, a new subclass of analytic and bi-univalent functions by means of Chebyshev polynomials is introduced. Certain coefficient bounds for functions belong to this subclass are obtained. Furthermore, the Fekete-Szegö problem in this subclass is solved.2010 Mathematics Subject Classification. Primary 30C45; Secondary 30C50.

A comprehensive subclass of bi-univalent functions associated with Chebyshev polynomials of the second kind

“…Now, we are ready to find the sharp bounds of Fekete-Szegö functional a 3 − ηa 2 2 defined for B µ Σ (λ, δ, t) given by (1.1). The results presented in this section improve or generalize the earlier results of Bulut et al [11], Yousef et al [30], and other authors in terms of the ranges of the parameter under consideration.…”

“…Corollary 3.6. [30] Let the function f (z) given by (1.1) be in the class B Σ (λ, t). Then |a 3 − a 2 2 | ≤ 2t 1 + 2λ .…”

“…Remark 1. Note that for λ = 1, µ = 1 and δ = 0, the class of functions B 1 Σ (1, 0, t) := B Σ (t) have been introduced and studied by Altinkaya and Yalçin [2], for µ = 1 and δ = 0, the class of functions B 1 Σ (λ, 0, t) := B Σ (λ, t) have been introduced and studied by Bulut et al [10], for δ = 0, the class of functions B µ Σ (λ, 0, t) := B µ Σ (λ, t) have been introduced and studied by Bulut et al [11], and for µ = 1, the class of functions B 1 Σ (λ, δ, t) := B Σ (λ, δ, t) have been introduced and studied by Yousef et al [30].…”

Faber polynomial coefficient estimates for a class of analytic bi-univalent functions

“…Thus, clearly, the image of the domain does not contain the unit disk U. For a brief history and some intriguing examples of functions and characterization of the class Σ, see Srivastava et al [19], Frasin and Aouf [11], and Yousef et al [24].…”

Initial bounds for analytic and bi-univalent functions by means of (p,q)−Chebyshev polynomials defined by differential operator

“…Recently, Kızılateş, Naim and Bayram [16] defined (p, q)−Chebyshev polynomials of the first and second kinds and derived explicit formulas, generating functions and some interesting properties of these polynomials.…”