Proof of an open inequality with double power-exponential functions

摘要

C?rtoaje (J. Nonlinear Sci. Appl. 4(2):130-137, 2011) conjectured that the inequality a ( 2 b ) x + b ( 2 a ) x ≤ 1 with double power-exponential functions holds for all nonnegative real numbers a, b with a + b = 1 and all x ≥ 1 . In this paper, we shall prove the conjecture affirmatively. MSC:26D10.