On <i>q</i>-Hermite-Hadamard Inequalities for Differentiable Convex Functions

Abstract

In this paper, we establish some new results on the left-hand side of the q-Hermite−Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 2018, 30, 193-203), by considering the critical point-type inequalities.

Keywords

• Hermite-Hadamard inequalities
• <i>q</i>-derivative
• <i>q</i>-integral
• convex functions