Initial bounds for analytic and bi-univalent functions by means of Chebyshev polynomials

Abstract

Abstract. In this paper, we obtain initial coefficient bounds for functions belong to a subclass of bi-univalent functions by using the Chebyshev polynomials and also we find Fekete-Szegö inequalities for this class.Mathematics subject classification (2010): 30C45.

Second Hankel determinant for certain class of bi-univalent functions defined by Chebyshev polynomials

“…The class N µ σ (λ, t) was introduced and studied by Bulut et al [9]. Also, they discussed initial coefficient estimates and Fekete-Szegö bounds for the class N µ σ (λ, t) and it's subclasses given in the following remark.…”

“…where the function g = f −1 is defined by (1.2) . This class was introduced and studied by Bulut et al [10] (see also [28]).…”

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

“…| for various classes of functions defined in terms of subordination (see e.g.,[1,20]). Motivated by the earlier work of Dziok et al[10], the main focus of this work is to utilize the Chebyshev polynomials expansions to solve Fekete-Szegö problem for certain subclass of bi-univalent functions (see, for example,[5,6,7,14]). …”

Coefficient estimates and Fekete-Szegö inequality for a class of analytic functions satisfying subordinate condition associated with Chebyshev polynomials

“…where n denotes the polynomial degree and x = cos θ. Applications of Chebyshev polynomials for analytic functions can be found in [1,2,3,4]. Let…”