Representations of Error Terms in Jensen's and Some Related Inequalities with Applications

Abstract

We give integral representations of error terms in the classical Jensen's inequality as well as in four related inequalities. Starting from these results, it is possible to derive various lower and upper asymptotic expansions for solutions of the functional equationf(x+1)-f(x)=g(x). In particular, we present several results concerning the gamma function. © 1999 Academic Press.