Open Access Research

Some generalizations of Aczél, Bellman's inequalities and related power sums

Xiaoyan Zhou

Author Affiliations

The School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China

Journal of Inequalities and Applications 2012, 2012:130 doi:10.1186/1029-242X-2012-130

Published: 8 June 2012

Abstract

In this paper, we establish some functional generalizations and refinements of Aczél's inequality and of Bellman's inequality. We also establish several mean value theorems for the related power sums.

Mathematics Subject Classification (2010): 26D15; 26D20; 26D99.

Keywords:
generalization; Aczél's inequality; Bellman's inequality; mean value theorem; power sums