The Hermite—Hadamard Inequality on Simplices

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

“…In our article we use the Hermite-Hadamard inequality on simplices, which was firstly given by Neuman [7], then reproved by Guessab and Schmeisser [3], Bessenyei [1] and the second-named author [13, Corollary 3]:…”

“…It was natural to generalize the Hermite-Hadamard inequality to functions of several variables. 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…”

Multi-dimensional Hadamard's inequalities

“…To prove (17), we will use a theorem in [1] that says the average of a convex function on a triangle is less than or equal to the average of the values of the function at the three vertices.…”

“…We extend our . The reader is referred to [5] and [6] for the original papers on Hadamard's inequality, and [1], [4], [7], [8], [9], [10] or [13] for some new developments on this topic.…”

Generalization of some inequalities via Riemann-Liouville fractional calculus

“…See [1], [2], [4], [6], [8], [10] and the references therein. Of special interest to us is the following improvements of the Hermite-Hadamard inequality, that can be found in the monograph [7], p. 52:…”