Generalized Laguerre Polynomial Bounds for Subclass of Bi-Univalent Functions

Abstract

In the present paper, we propose to introduce a new subclass of bi-univalent analytic functions T_∑(λ, γ) (0 < λ ≤ 1, γ ≥ 0) which is defined by making use of the generalized Laguerre polynomials in the open unit disk ∇. We derive upper bounds for the coefficients |a₂|, |a₃| and discuss Fekete-Szeg¨o problem for the functions belonging to the new introduced class T_∑(λ, γ).

Key words and phrases. Analytic functions, Bi-univalent functions, Generalized Laguerre polynomial, Generating function, Fekete-Szeg¨o inequality, Principle of subordination.

2010 Mathematics Subject Classification. Primary: 30C45, 33C45; Secondary 30C50