Optimal Inequalities for the Convex Combination of Error Function
نویسندگان
چکیده
For λ ∈ (0,1) and x,y > 0 we obtain the best possible constants p and r , such that erf(Mp(x,y;λ)) λ erf(x)+(1−λ) erf(y) erf(Mr(x,y;λ)) where erf(x) = 2 √π ∫ x 0 e −tdt and Mp(x,y;λ) = (λxp + (1− λ)yp)1/p(p = 0) , M0(x,y;λ) = xλ y1−λ are error function and weighted power mean, respectively. Furthermore, using these results, we generalized and complement an inequality due to Alzer.
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