Inequalities between sum of the powers and the exponential of sum of nonnegative sequence

Abstract

In this paper, we give a generalization of results of F. Qi [1].We obtain by using a short proof, the following inequality between the sumof power and the exponential of sum of nonnegative sequenceepppn∑i=1xpi≤exp(n∑i=1xi),wherep≥1, n≥2, xi≥0 for 1≤i≤n,and the constantepppis the bestpossible.