[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2012.52.4.495

Improvement of Jensen's Inequality in terms of Gâteaux Derivatives for Convex Functions in Linear Spaces with Applications

Khan, Muhammad Adil (Department of Mathematics, University of Peshawar)
Khalid, Sadia (Abdus Salam School of Mathematical Sciences, GC University)
Pecaric, Josip (Faculty of Textile Technology, University of Zagreb)

Publication Information

Kyungpook Mathematical Journal / v.52, no.4, 2012 , pp. 495-511 More about this Journal

Abstract

In this paper, we prove some inequalities in terms of G $\hat{a}$ teaux derivatives for convex functions defined on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give applications for norms, mean $f$ -deviations and $f$ -divergence measures.

Keywords

Convex functions; G $\hat{a}$ teaux derivatives; Jensen's inequality; Norms; Mean f-deviations; f-Divergence measures;

Citations & Related Records

Reference

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