On strongly starlike and convex functions of order alpha and type beta

TL;DR

This paper explores the relationship between strongly starlike and strongly convex functions of certain orders and types, providing new insights and applications within the theory of normalized analytic functions on the unit disk.

Contribution

It establishes inclusion relationships between classes of strongly starlike and strongly convex functions of specified order and type, extending classical results in geometric function theory.

Findings

Established inclusion relationships between function classes.

Presented applications of the main results to classical subclasses.

Extended understanding of the structure of starlike and convex functions.

Abstract

In this note we investigate the inclusion relationship between the class of strongly starlike functions of order alpha and type beta and the class of strongly convex functions of order alpha and type beta which are subclass of normalized analytic functions defined on the unit disk. Some applications of our main result are also presented which contains various classical results for the typical subclasses of starlike and convex functions.