Generalized Hermite-Hadamard-Mercer type inequalities via majorization

Abstract

The Hermite-Hadamard inequality has been recognized as the most pivotal inequality which has grabbed the attention of several mathematicians. In recent years, load of results have been established for this inequality. The main theme of this article is to present generalized Hermite-Hadamard inequality via the Jensen-Mercer inequality and majorization concept. We establish Hermite-Hadamard inequality of the Jensen-Mercer type for majorized tuples. With the aid of weighted generalized Mercer's inequality, we also prove weighted generalized Hermite-Hadamard inequality for certain tuples. The idea of obtaining the results of this paper, may explore a new way for derivation of several other results for Hermite-Hadamard inequality.