Monotonicity, Convexity and Inequalities Involving the Generalized Elliptic Integrals

By Miao-Kun Wang, Wen Zhang, Y. Chu. Acta Mathematica Scientia, 2019

81 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/10068541b4b1eed966384349d16da93d88465c3c

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Citations in the corpus

Ostrowski type inequalities in the sense of generalized $\mathcal{K}$-fractional integral operator for exponentially convex functions (2020, background): “There are numerous problems wherein fractional derivatives (non-integer order derivatives and integrals) attain a valuable position [4, 5, 8, 16, 24, 27, 31, 36, 41, 60, 62, 63, 70].”
Answers to three conjectures on convexity of three functions involving complete elliptic integrals of the first kind (2020, background): “Because of the great importance of these integrals, Vourinen and his collaborators initiated an independent subject to study the complete elliptic integrals and their related special functions, numerous new properties and inequalities involving K(r) and E(r) have been obtained in recent years [16, 1”
Some New Hermite–Hadamard-Type Inequalities Associated with Conformable Fractional Integrals and Their Applications (2020, unknown): “φ λd1 +(1 − λ)d2 ( 􏼁 − 1 d2 − d1 􏽚 d2 d1 φ(s)ds 􏼌􏼌􏼌􏼌􏼌􏼌􏼌 􏼌􏼌􏼌􏼌􏼌􏼌􏼌 ≤ (1 − λ) A1(1, p) ( 􏼁 1/p E 1/q 1 􏽨 􏽩 + λ A2(1, p) ( 􏼁 1/p E 1/q 2 􏽨 􏽩, (23) where A1(α, P), A2(α, P), E1(α), and E2(α) are defined as in .”
Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means (2020, background): “is the complete elliptic integral of the second kind [12,18,30,38,44,50,52] and it is the special case of the Gaussian hypergeometric function [31,41,42,49,57]”