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



Hiroshima Mathematical Journal

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

R. Parvatham, S. Ponnusamy and S. K. Sahoo

Source: Hiroshima Math. J. Volume 38, Number 1 (2008), 19-29.

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.

Primary Subjects: 30C45
Secondary Subjects: 30C55, 33C05
Keywords: Bernardi transform; univalent; starlike and convex functions; hypergeometric function

Full-text: Access granted (open access)

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.hmj/1207580342


2008 © Hiroshima University, Department of Mathematics