Convexity of the complete elliptic ingegrals of the first kind with respect to Holder means

By 蒋月评, 王淼坤, 褚玉明, 裘松良. 2012

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Sharp power mean bounds for the lemniscate type means (2021, background): “33020 [9] Wang, M-K; Chu, Y-M; Qiu, S-L; Jiang, Y-P, Convexity of the complete elliptic integrals of the first kind with respect to Hölder means, J.”
Some new inequalities of Hermite-Hadamard type for s-convex functions with applications (2017, unknown): “Recently, the improvements, generalizations, refinements and applications for the Hermite-Hadamard inequality have attracted the attention of many researchers [23-41].”
Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means (2020, background): “The complete elliptic integral K(r) (0 < r < 1) [1,7,8,11,23,27,32,39,40,43,46,48,51] of the first kind is closely related to the complete elliptic integral E(r) of the second kind, which is defined by”