Mihály Bessenyei

TL;DR: In this paper, the authors investigate (ω 1,ω 2 ) -convex functions and obtain characterization theorems and Hadamard-type inequalities for them, and show that these inequalities are equivalent to the same properties for (ω 2,ω 3 ) functions.

TL;DR: The aim of the present paper is to verify Hadamard's inequality on simplices via an elementary approach, independently of Choquet's Theory, and finds that the volume of a triangular prism whose top is not necessarily parallel to the plane of the base can be calculated as the product of thebase's area and the average of the prism's edges.

TL;DR: In this paper, the Hermite-Hadamard inequality is applied to generalized convexity induced by two-dimensional Chebyshev systems, and a characterization theorem of continuous, non-convex functions is presented.

TL;DR: In this article, the Hermite-Hadamard type inequalities for generalized convex functions were established for Tcheby-chev systems, based on moment spaces induced by Tchebyschev systems.

TL;DR: In this article, a generalization of Hadamard's classical in-equality for higher-order convex functions is presented. But this generalization relies on the Hermite-Fejer interpolation.