ACTA issues

Some inequalities for $f$-divergence measures generated by $2n$-convex functions

Sever S. Dragomir, Stamatis Koumandos

Acta Sci. Math. (Szeged) 76:1-2(2010), 71-86

Abstract. A double Jensen type inequality for $2n$-convex functions is obtained and applied to establish upper and lower bounds for the $f$-divergence measure in Information Theory. Some particular inequalities of interest are stated as well.

AMS Subject Classification (1991): 94Axx, 26D15, 26D10

Keyword(s): $f$-divergence measure, $2n$-convexity, convex functions, absolutely monotonic and completely monotonic functions, analytic inequalities

Received September 10, 2008, and in final form October 13, 2009. (Registered under 56/2010.)