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Turkish Journal of Mathematics

DOI

10.3906/mat-1905-71

Abstract

Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n-strongly convex functions using extended idea of convexity to the class of strongly convex functions. We also obtain upper bound for Sherman's inequality, called the converse Sherman inequality, and as easy consequences we get Jensen's as well as majorization inequality and their conversions for strongly convex functions. Obtained results are stronger versions for analogous results for convex functions. As applications, we introduced a generalized concept of f-divergence and derived some reverse relations for such concept.

Keywords

Jensen inequality, convex function, strongly convex function, majorization, Sherman inequality

First Page

2680

Last Page

2696

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