Open Access

New Means of Cauchy's Type

Journal of Inequalities and Applications20082008:163202

DOI: 10.1155/2008/163202

Received: 30 December 2007

Accepted: 7 April 2008

Published: 16 April 2008

Abstract

We will introduce new means of Cauchy's type defined, for example, as in the case when , . We will show that this new Cauchy's mean is monotonic, that is, the following result. Theorem. Let , such that , . Then for , one has . We will also give some related comparison results.

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Authors’ Affiliations

(1)
Abdus Salam School of Mathematical Sciences, GC University
(2)
Faculty of Textile Technology, University of Zagreb

Copyright

© M. Anwar and J. Pečarć. 2008

This article is published under license to BioMed Central Ltd. 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.