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

Soft Computing - 2022
Necmettin Alp1, Hüseyin Budak1, Samet Erden2, Mehmet Zeki Sarıkaya1
1Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
2Department of Mathematics, Faculty of Science, Bartın University, Bartin, Turkey

Tóm tắt

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 $$q\rightarrow 1^{-}.$$

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