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