On Csiszár and Tsallis type f-divergences induced by superquadratic and convex functions

Abstract

Abstract. In this paper, Csiszár and Tsallis f -divergences are studied for superquadratic and convex functions. Some comparison theorems for two divergences are provided. The obtained results, when used for nonnegative superquadratic functions, give some refinements of the original inequalities corresponding to nonnegative convex functions. Some majorization assumptions for the involved matrix are simplified from column stochasticity to entrywise-nonnegativity.Mathematics subject classification (2010): 26D15, 15B51, 94A17.

Inequalities for Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal Type f–Divergences

“…The Csiszár f-divergence is defined by (see [ 15 ]) with the conventions and , (see [ 18 , 19 , 20 ]).…”

“…This paper is based on publications in which we introduced new types of f -divergences [ 13 , 14 , 15 , 16 ].…”