On some new and general q-Hermite–Hadamard type inequalities for convex functions

Abstract

In this paper, we establish a new version of Hermite–Hadamard type inequality for convex functions. Moreover, we establish a general version of q-integral identity involving q-differentiable functions to prove some new q-midpoint and q-trapezoidal type inequalities for q-differentiable convex functions. It is also shown that the newly established inequalities can be converted into some existing inequalities within the literature. Finally, we add some mathematical examples to show the validation of newly established inequalities.