A refinement of the left-hand side of Hermite-Hadamard inequality for simplices

Abstract

In this paper, we establish a new refinement of the left-hand side of Hermite-Hadamard inequality for convex functions of several variables defined on simplices. MSC: Primary 26D15

Improvements of the Hermite-Hadamard inequality for the simplex

“…Similar inequalities concerning the standard n -simplex were obtained in [5, 6] and [18]. Special refinements of the left and right-hand side of the Hermite-Hadamard inequality were recently obtained in [19] and [20]. …”

Another refinement of the right-hand side of the Hermite–Hadamard inequality for simplices

“…Just for completeness note that similar refinement of the left-hand side of (1) can be found in [4,Corollary 2.6]. It reads as follows:…”

Applications of the Hermite-Hadamard inequality

“…Note that the simplices ∆ [K] can be obtained by applying homotheties to the faces of ∆. The details are explained in [7].…”

“…also received generalizations for simplices [10], disks, 3-balls and regular n-gons P [2]: In this paper we use the lower and upper estimates for the average of a convex function over a simplex obtained by the authors in [7,8] to provide the alternate proof of the above results and to generalize then to figures and bodies satisfying some regularity conditions and to broader class of functions.…”