Differential Subordination implications for Certain Carath\'{e}odory functions

TL;DR

This paper establishes differential subordination relations for Carathéodory functions with geometric properties, leading to implications that classify normalized analytic functions into various starlike subclasses.

Contribution

It introduces new differential subordination relations for Carathéodory functions and explores their implications for classifying starlike functions.

Findings

Derived first order differential subordination relations

Identified implications for subclasses of starlike functions

Enhanced understanding of geometric properties of Carathéodory functions

Abstract

In this article, we wish to establish some first order differential subordination relations for certain Carath\'{e}odory functions with nice geometrical properties. Moreover, several implications are determined so that the normalized analytic function belongs to various subclasses of starlike functions.