A lower bound of the power exponential function

Abstract

. In this paper, we consider the lower bound of the power exponential function a 2 b + b 2 a for nonnegative real numbers a and b . If a + b = 1, then it is known that the function has the maximum value 1, but it is no known that the minimum value. In this paper, we show that a 2 b + b 2 a > 6083 / 6144 ∼ = 0 . 990072 for nonnegative real numbers a and b with a + b = 1.