On New Estimates of <i>q</i>-Hermite–Hadamard Inequalities with Applications in Quantum Calculus

Abstract

In this paper, we first establish two quantum integral (q-integral) identities with the help of derivatives and integrals of the quantum types. Then, we prove some new q-midpoint and q-trapezoidal estimates for the newly established q-Hermite-Hadamard inequality (involving left and right integrals proved by Bermudo et al.) under q-differentiable convex functions. Finally, we provide some examples to illustrate the validity of newly obtained quantum inequalities.

Keywords

• Hermite-Hadamard inequality
• q-integral
• quantum calculus
• convex function