New Quantum Hermite–Hadamard-Type Inequalities for p-Convex Functions Involving Recently Defined Quantum Integrals

Abstract

We develop new Hermite–Hadamard-type integral inequalities for p-convex functions in the context of q-calculus by using the concept of recently defined T_q-integrals. Then the obtained Hermite–Hadamard inequality for p-convex functions is used to get a new Hermite–Hadamard inequality for coordinated p-convex functions. Furthermore, we present some examples to demonstrate the validity of our main results. We hope that the proposed ideas and techniques may stimulate further research in this field.