Logarithmic convexity of extended mean values

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ON CERTAIN MEANS OF TWO ARGUMENTS AND THEIR EXTENSIONS (2003, unknown): “(See [4, 12, 23]).”
NOTES ON THE SCHUR-CONVEXITY OF THE EXTENDED MEAN VALUES (2005, unknown): “In [11], the ﬁrst author veriﬁed the logarithmic convexity of the extended mean values E ( r, s ; x, y ) with two parameters r and s as follows.”
The Best Bounds in Gautschi-Kershaw Inequalities (2006, unknown): “The positive function g a , b ( u ) has been researched in [ 18 ] and was applied in [ 7, 10, 12, 17 ] to prove the logarithmic convexity or the Schur convexity of the extended mean values.”
An alternative note on the Schur-convexity of the extended mean values (2006, methodology): “The logarithmic convexity of the extended mean values E(r, s;x, y) with two parameters r and s was obtained in [12, 13].”
Bounds for the Ratio of Two Gamma Functions (2009, methodology): “) 6= 0; E(0,0;x,y) = √ xy, x6= y; E(r,s;x,x) = x, x= y. (3.7) Actually, the inequality (3.6) is an immediate consequence of monotonicity of E(r,s;x,y), see [30]. For more information, please refer to [13, 17, 23, 33, 38, 39, 47, 48, 50, 51, 58, 70, 71, 73, 74, 75, 78] and related references therein.”
Complete Monotonicities of Functions Involving the Gamma and Digamma Functions (2004, unknown): “For more information, please refer to [14, 15, 18, 23, 25] and references therein.”