International Journal of Mathematics and Mathematical Sciences

Volume 15 (1992), Issue 3, Pages 441-447

doi:10.1155/S0161171292000590

## A majorant problem

# Ronen Peretz

Department of Mathematics, University of Michigan, Ann Arbor 48109, MI, USA

Received 25 September 1990

Copyright © 1992 Ronen Peretz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Let

In this paper we study the problem of maximizing the

It is proved that a maximizing function is

One consequence of our paper is that for

We also give some applications to derive some sharp inequalities for the classes of Schlicht functions and of functions of positive real part.