%0 Journal Article
%T Estimations of the Lehmer mean by the Heron mean and their generalizations involving refined Heinz operator inequalities
%J Advances in Operator Theory
%I Tusi Mathematical Research Group (TMRG)
%Z 2538-225X
%A Ito, Masatoshi
%D 2018
%\ 10/01/2018
%V 3
%N 4
%P 763-780
%! Estimations of the Lehmer mean by the Heron mean and their generalizations involving refined Heinz operator inequalities
%K Lehmer mean
%K Heron mean
%K power difference mean
%K operator mean
%K Heinz operator inequalities
%R 10.15352/aot-1801-1303
%X As generalizations of the arithmetic and the geometric means, for positive real numbers $a$ and $b$,the power difference mean $J_{q}(a,b)=frac{q}{q+1}frac{a^{q+1}-b^{q+1}}{a^{q}-b^{q}}$,the Lehmer mean $L_{q}(a,b)=frac{a^{q+1}+b^{q+1}}{a^{q}+b^{q}}$ and the Heron mean $K_{q}(a,b)=(1-q)sqrt{ab}+qfrac{a+b}{2}$ are well known.In this paper, concerning our recent results on estimations of the power difference mean, we obtain the greatest value $alpha=alpha(q)$ and the least value $beta=beta(q)$ such that the double inequalityfor the Lehmer mean [K_{alpha}(a,b)