Derivation of Conticrete Hermite-Hadamard-Jensen-Mercer Inequalities Through k-Caputo Fractional Derivatives and Majorization

Abstract

The Hermite-Hadamard inequality stands out as one of the highly valuable inequalities due to its exceptional role in research.
Many mathematicians are working hard right now to create various improvements, generalizations and extensions of this inequality.
This study develops the Hermite-Hadamard-Jensen-Mercer inequalities in a conticrete framework through the application of k-Caputo fractional derivatives and the concept of majorization. These inequalities are also presented in their weighted forms by assuming certain monotonic tuples.
Furthermore, the setting of bounds for the discrepancy of the terms of our important inequalities is also accomplished on the basis of the two newly deduced identities.