Table of Contents
ISRN Mathematical Analysis
Volume 2014 (2014), Article ID 272405, 8 pages
http://dx.doi.org/10.1155/2014/272405
Research Article

Some Inequalities for Polynomials Not Vanishing inside a Circle

Department of Mathematics, University of Kashmir, Hazratbal Srinagar 190006, India

Received 18 January 2014; Accepted 16 February 2014; Published 19 May 2014

Academic Editors: K. A. Lurie and M. A. McKibben

Copyright © 2014 Abdullah Mir and Bilal Dar. 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

If is a polynomial of degree having no zeros in , then it is known that, for all with , , , and , . In this paper, we will prove a result which not only generalizes the above inequality but also generalize and refines the various results pertaining to the norm of . We will also prove a result which extends and refines a result of Boas Jr. and Rahman (1962). Also we will see that our results lead to some striking conclusions giving refinements and generalizations of other well-known results.