This analysis establishes symmetric midpoint inequalities for differentiable convex functions, suggesting potential for further exploration in mathematical inequalities.
In this study, we first develop symmetric quantum integral identity utilizing the derivatives and integrals of symmetric quantum types. Then, by using this identity, we establish modified versions of midpoint-type inequalities for differentiable convex functions. To obtain recent results, a few basic inequalities such as power mean and H?lder?s, have been utilized. We create links between our results and previous findings in the literature taking q ? 1. For a better understanding and validation of the results, we present numerical results and some graphs. Finally, we provide some examples to illustrate the validity of newly obtained symmetric quantum inequalities. The concepts and methods presented in this work can inspire more investigation.
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Hussain et al. (2025) studied this question.
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