ON A GENERALIZED UPPER BOUND FOR THE EXPONENTIAL FUNCTION

Abstract

With the introduction of a new parameter n≥ 1, Kim generalized an upper bound for the exponential function that implies the inequality between the arithmetic and geometric means. By a change of variable, this generalization is equivalent to exp

n(x−1) n+x−1

≥ n−1+xn n for real n ≥ 1 and x > 0. In this paper, we show that this inequality is true for real x > 1 − n provided that n is an even integer.