TY - JOUR
ID - 60974
T1 - Estimations of the Lehmer mean by the Heron mean and their generalizations involving refined Heinz operator inequalities
JO - Advances in Operator Theory
JA - AOT
LA - en
SN -
A1 - Ito, Masatoshi
Y1 - 2018
PY - 2018/10/01
VL - 3
IS - 4
SP - 763
EP - 780
KW - Lehmer mean
KW - Heron mean
KW - power difference mean
KW - operator mean
KW - Heinz operator inequalities
DO - 10.15352/aot-1801-1303
N2 - 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)