Sharp bounds for Toader mean in terms of arithmetic, quadratic, and Neuman means

摘要

In this paper, we present the best possible parameters α , β ∈ R $lpha, eta inmathbb{R}$ and λ , μ ∈ ( 1 / 2 , 1 ) $lambda, muin(1/2, 1)$ such that the double inequalities α N A Q ( a , b ) + ( 1 − α ) A ( a , b ) T ∗ ( a , b ) β N A Q ( a , b ) + ( 1 − β ) A ( a , b ) $lpha N_{AQ}(a,b)+(1-lpha)A(a,b) T^{st}(a,b)eta N_{AQ}(a,b)+(1-eta)A(a,b)$ , Q [ λ a + ( 1 − λ ) b , λ b + ( 1 − λ ) a ] T ∗ ( a , b ) Q [ μ a + ( 1 − μ ) b , μ