Differential subordination and convexity criteria of integral operators

Abstract

A significant connection between certain second-order differential subordination and subordination of f′(z) is obtained. This fundamental result is next applied to investigate the convexity of analytic functions defined in the open unit disk. As a consequence, criteria for convexity of functions defined by integral operators are determined. Connections are also made to earlier known results.

Keywords

• convex functions
• differential subordination
• integral operators
• 30c45
• 30c80