Initial bounds for certain subclasses of generalized salagean type Bi-univalent functions associated with the Horadam polynomials

Abstract

This study proposes the use of Horadam polynomials which are known as their special cases, such as the Fibonacci polynomials, the Lucas polynomials, the Pell polynomials, the Pell-Lucas polynomials, and Chebyshev polynomials of the second kind. The aim of this study is to introduce a new subclass of generalized Sǎlǎgean type bi-univalent functions using Hadamard product and defined by Horadam polynomials ()nx in the open unit disk {z:1}.UCz We obtained coefficient estimates of the Taylor-Maclaurin 2a and 3a for functions f belonging to this newly defined subclass. Fekete-Szegö inequalities were also studied. Moreover, we give some interesting results using the relation between Sǎlǎgean’s differential operator and generalized Sǎlǎgean differential operator.