A Quantum Calculus View of Hermite–Hadamard–Jensen–Mercer Inequalities with Applications

Abstract

In this paper, we derive some new quantum estimates of generalized Hermite–Hadamard–Jensen–Mercer type of inequalities, essentially using q-differentiable convex functions. With the help of numerical examples, we check the validity of the results. We also discuss some special cases which show that our results are quite unifying. To show the efficiency of our main results, we offer some interesting applications to special means.

Keywords

• convex function
• quantum calculus
• Jensen–Mercer inequalities
• differentiable function
• means