On some inequalities equivalent to the Wright-convexity

Abstract

Abstract. In the present paper we establish some conditions and inequalities equivalent to the Wright-convexity.Mathematics subject classification (2010): 39B62, 26A51, 26B25.

On certain Schur-convex functions

“…gives Wright-convexity; (for more information about Wright-convexity, see e.g. [Wri54], [Ng87], [MNP91], [Olb06], [Olb11], [Olb15b], and the references therein);…”

“…Since then, a vast number of publications has been printed using Schur-convexity from different areas of mathematics, including real function theory (e.g. [Olb15b]), inequalities (e.g. [Ste07]), financial mathematics (e.g.…”

Convexity properties of functions defined on metric Abelian groups

“…The structure and properties of t-convex sets and t-quasiconvex, t-Wright convex, and t-convex functions and their generalizations have been investigated in a large number of recent papers, see e.g. [1,6,7,9,10,[12][13][14][15][16][17][18][19][20][21][22][23]25,[27][28][29][30][31][32][33][34][35]39].…”

Hermite-Hadamard type inequalities for Wright-convex functions of several variables

“…Because the note [10] is actually unpublished, let us mention that (1.1) is an immediate consequence of the Hermite-Hadamard inequality. It is enough to apply it to the convex (due to Ng'…”

“…In the case of simplices, for the first time it was done by Neuman [7] (see also [1,3] and [13] for the functions defined on simplices and [2,9] for more general domains). Recently Olbryś [10] obtained the following inequality of Hermite-Hadamard type: if f : I → R (where I ⊂ R is an open interval) is W-convex, then…”