Radius of convexity for integral operators involving Hornich operations

Abstract

The objective of the present paper is to determine the sharp radii of convexity for the integral operator [Formula presented] when f and g range over some classes of classical analytic functions defined in the open unit disk |z|<1 with f(0)=0. Here, the exponents are chosen in such a way that the respective functions are analytic in suitable branches. As an importance of considering the operator Cα,β, we observe the radii of convexity in some classical situations through several consequences of our main results. © 2021 Elsevier Inc.