On q-Hermite–Hadamard–Mercer and midpoint-Mercer inequalities for general convex functions with their computational analysis

This paper establishes some new inequalities of Hermite–Hadamard–Mercer type for [Formula: see text]-convex functions in the framework of [Formula: see text]-calculus and classical calculus. Some new [Formula: see text]-midpoint-Mercer type inequalities for the [Formula: see text]-differentiable [Formula: see text]-convex functions are also proved. Moreover, the computational analysis of newly established inequalities for convex and [Formula: see text]-convex functions are given to prove that the bounds of this paper are better than those of the existing ones. It is also shown with mathematical examples that the newly established inequalities are valid for [Formula: see text]-convex functions in [Formula: see text]-calculus.