New bounds for q-midpoint-type inequalities via twice q-differentiable functions on quantum calculus

Abstract

The aim of this work is to establish new bounds for q-midpoint-type integral inequalities for twice q-differentiable convex functions. We first prove some lemmas which are useful for our main results. Then, we present some midpoint-type inequalities for twice q-differentiable functions. With all these, we showed the results we found in the classical analysis by using q -> 1(-).