Applications of q-Derivative Operator to the Subclass of Bi-Univalent Functions Involving q-Chebyshev Polynomials

Abstract

In recent years, the usage of the q-derivative and symmetric q-derivative operators is significant. In this study, firstly, many known concepts of the q-derivative operator are highlighted and given. We then use the symmetric q-derivative operator and certain q-Chebyshev polynomials to define a new subclass of analytic and bi-univalent functions. For this newly defined functions' classes, a number of coefficient bounds, along with the Fekete-Szego inequalities, are also given. To validate our results, we give some known consequences in form of remarks.