New generalization of H. Alzer's inequality

Abstract

A new generalization of H. Alzer's inequality is proved. This inequality generalizes both results in an article by N. Elezovic and J. Pecaric (J. Math. Anal. Appl. 223 (1998), 366--369) as well as an article by Feng Qi (J. Math. Anal. Appl. 240 (1999), 294--297). It is shown that this inequality is satisfied for a large class of increasing convex sequences.