Sharp two-parameter bounds for the identric mean

摘要

For t∈[0,1/2] and s≥1, we consider the two-parameter family of means Qt,s(a,b)=Gs(ta+(1−t)b,(1−t)a+tb)A1−s(a,b), where A and G denote the arithmetic and geometric means. Sharp bounds for the identric mean in terms of Qt,s are obtained. Our results generalize and extend bounds due to Chu et al. (Abstr. Appl. Anal. 2011:657935, ) and to Wang et al. (Appl. Math. Lett. 25:471–475, ).