Monotonicity theorems and inequalities for the complete elliptic integrals

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Optimal Lehmer Mean Bounds for the Toader Mean (2011, background): “In [3], Alzer and Qiu presented a best possible upper power mean bound for the Toader mean as follows: T (a, b) < Mlog 2/log (π/2)(a, b) (1.”
A Power Mean Inequality involving the complete elliptic integrals (2013, background): “Numerous sharp inequalities and elementary approximations for the complete elliptic integrals have been proved in [2, 3, 7, 8, 13, 14].”
Hölder mean inequalities for the complete elliptic integrals (2012, background): “In particular, many remarkable properties and inequalities for K and E can be found in the literature [1,3,4,7,10,12,17,23,27,28,30].”
Full length article: Bounds for the perimeter of an ellipse (2012, background): “In 2004, Alzer and Qiu [3] gave a better upper bound for L(a, b) as follows: L(a, b) < 2π Mlog 2/ log(π/2)(a, b) (3.”
Turán type inequalities for generalized complete elliptic integrals (2007, background): “Very recently, in 2004 the left-hand side of inequality (3.2) was improved by Alzer and Qiu [ 2 ].”
Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means (2020, background): “[11] CHU, Y.-M.—WANG, M.-K.—QIU, Y.-F.: On Alzer and Qiu’s conjecture for complete elliptic integral and inverse hyperbolic tangent function, Abstr.”