Some New Improvements for Fractional Hermite–Hadamard Inequalities by Jensen–Mercer Inequalities

Abstract

This article’s objective is to introduce a new double inequality based on the Jensen–Mercer JM inequality, known as the Hermite–Hadamard–Mercer inequality. We use the JM inequality to build a number of generalized trapezoid-type inequalities. Moreover, in addition to the JM inequality, we also use the Hölder inequality and the power mean inequality. Finally, a few examples are given to highlight the main points of our outcomes.