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–Szegö inequalities, are also given. To validate our results, we give some known consequences in form of remarks.