On New Subclasses of Analytic Functions Involving (p,q)-Derivatives

Abstract

Objective:The objectives of the present study are to introduce some new subclasses of analytic functions involving (p,q)-derivatives by using subordination. We derive Fekete-Szegö inequalities for the functions belonging to the new subclasses. Method: Using the concept of (p,q)-derivative of a function and the subordination principle between analytic functions we introduce and study new subclasses. Findings: The Fekete-Szegö problem may be considered as one of the most important results about univalent functions. It was introduced by Fekete-Szegö in 1933. Coefficient estimates for the second and third coefficients of functions belonging to class of analytic functions with specific geometric properties were obtained. We obtain the Fekete-Szegö inequalities for functions belonging to the new subclasses. Moreover, some special cases of the established results are discussed. Novelty: The results of the paper are new and significantly contribute to the existing literature on the topic.