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Original Article

Kyungpook Mathematical Journal 2012; 52(4): 495-511

Published online December 23, 2012

Copyright © Kyungpook Mathematical Journal.

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

Muhammad Adil Khan1, Sadia Khalid2, Josip Pecaric3

1Department of Mathematics, University of Peshawar, Pakistan
2Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore 54600
3Pakistan, Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovica 28a, 10000 Zagreb, Croatia

Received: December 23, 2012; Revised: December 23, 2012; Accepted: December 23, 2012


In this paper, we prove some inequalities in terms of Gâteaux 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, Gâ,teaux derivatives, Jensen's inequality, Norms, Mean f-deviations, f-Divergence measures