First-order differential subordinations associated with Carathéodory functions

Abstract

In the present paper, we investigated some conditions to be in the class of Carathéodory functions by using the concept of the first-order differential subordinations. Moreover, various interesting special cases were considered in the geometric function theory as applications of main results presented here.

Keywords

• differential subordination
• carathéodory function
• univalent function
• starlike function of order alpha
• strongly starlike function