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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.)
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