A stronger inequality of Cˆırtoaje’s one with power exponential functions

In this paper, we will show that (a^{2b} + b^{2a} + r (ab(a b))^2 leq 1 ) holds for all (0 leq a) and (0 leq b) with (a + b = 1) and all (0 leq r leqfrac{1}/{2}). This gives the first example of a stronger inequality of (a^{2b} +b^{2a} leq 1).