Improvement of Jensens Inequality in terms of Gâteaux Derivatives for Convex Functions in Linear Spaces with Applications

• Journal title : Kyungpook mathematical journal
• Volume 52, Issue 4,  2012, pp.495-511
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2012.52.4.495
Title & Authors
Improvement of Jensens Inequality in terms of Gâteaux Derivatives for Convex Functions in Linear Spaces with Applications

Abstract
In this paper, we prove some inequalities in terms of G$\small{\hat{a}}$teaux derivatives for convex functions defined on linear spaces and also give improvement of Jensens inequality. Furthermore, we give applications for norms, mean $\small{f}$-deviations and $\small{f}$-divergence measures.
Keywords
Convex functions;G$\small{\hat{a}}$teaux derivatives;Jensens inequality;Norms;Mean f-deviations;f-Divergence measures;
Language
English
Cited by
1.
Further Refinements of Jensen’s Type Inequalities for the Function Defined on the Rectangle, Abstract and Applied Analysis, 2013, 2013, 1
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