Open Access Research

Quasilinearity of some functionals associated with monotonic convex functions

SS Dragomir

Author Affiliations

School of Engineering & Science, Victoria University, P.O. Box 14428, Melbourne City, MC 8001, Australia

School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits, P.O. Box 14428, Johannesburg, 2050, South Africa

Journal of Inequalities and Applications 2012, 2012:276 doi:10.1186/1029-242X-2012-276

Published: 28 November 2012

Abstract

Some quasilinearity properties of composite functionals generated by monotonic and convex/concave functions and their applications in improving some classical inequalities such as the Jensen, Hölder and Minkowski inequalities are given.

MSC: 26D15.

Keywords:
additive; superadditive and subadditive functionals; convex functions; Jensen’s inequality; Hölder’s inequality; Minkowski’s inequality