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−1+xn 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.

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