A NOTE ON A CERTAIN BIVARIATE MEAN

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Bounds of the Neuman-Sándor Mean Using Power and Identric Means (2013, background): “Neuman [25] and Zhao et al.”
OPTIMAL BOUNDS FOR NEUMAN-S ´ ANDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF LOGARITHMIC AND QUADRATIC OR CONTRA-HARMONIC MEANS (2014, unknown): “In [4], Neuman proved that the double inequalities αQ(a,b)+ (1−α)A(a,b) < M(a,b) < βQ(a,b)+ (1−β )A(a,b) and λC(a,b)+ (1−λ )A(a,b)< M(a,b) < μC(a,b)+ (1− μ)A(a,b) hold for all a,b > 0 with a = b if and only if α [1− log(1+√2)]/[(√2−1) log(1+ √ 2)] = 0.”