Fekete-Szego inequality for Classes of Starlike and Convex Functions

TL;DR

This paper introduces generalized classes of (p,q)-starlike and (p,q)-convex functions using the (p,q)-derivative operator, investigates Fekete-Szego inequalities, and explores applications of the (p,q)-Bernardi integral operator.

Contribution

It defines new classes of functions and derives Fekete-Szego inequalities within the (p,q) calculus framework, extending existing theories.

Findings

Derived Fekete-Szego inequalities for (p,q)-starlike and convex functions.

Discussed special cases and applications of the main results.

Applied the (p,q)-Bernardi integral operator to obtain further insights.

Abstract

In the present paper, the new generalized classes of (p,q)-starlike and $(p,q)$-convex functions are introduced by using the (p,q)-derivative operator. Also, the (p,q)-Bernardi integral operator for analytic function is defined in an open unit disc. Our aim for these classes is to investigate the Fekete-Szego inequalities. Moreover, Some special cases of the established results are discussed. Further, certain applications of the main results are obtained by applying the (p,q)-Bernardi integral operator