Applications of First-Order Differential Subordination for Subfamilies of Analytic Functions Related to Symmetric Image Domains

Abstract

This paper presents a geometric approach to the problems in differential subordination theory. The necessary conditions for a function to be in various subfamilies of the class of starlike functions and the class of Carathéodory functions are studied, respectively. Further, several consequences of the findings are derived.

Keywords

• analytic function
• differential subordination
• starlike function
• symmetric image domain