Norm estimates for the Bernardi integral transforms of functions defined by subordination

Abstract

In this paper, we obtain sharp norm estimates for the Bernardi integral transform of functions belonging to the class ${\mathcal K}(A,B)$, $-1\le B<A\le 1$, which is a subclass of the well-known class of convex univalent functions. As a consequence, a number of open questions arise naturally, concerning ${\mathcal S}^*(A,B)$--a subclass of the well-known class of starlike univalent functions, and many other classes.