Some Hermite-Hadamard and midpoint type inequalities in symmetric quantum calculus

Abstract

The Hermite-Hadamard inequalities are common research topics explored in different dimensions. For any interval $ [\mathrm{b_{0}}, \mathrm{b_{1}}]\subset\Re $, we construct the idea of the Hermite-Hadamard inequality, its different kinds, and its generalization in symmetric quantum calculus at $ \mathrm{b_{0}}\in[\mathrm{b_{0}}, \mathrm{b_{1}}]\subset\Re $. We also construct parallel results for the Hermite-Hadamard inequality, its different types, and its generalization on other end point $ \mathrm{b_{1}} $, and provide some examples as well. Some justification with graphical analysis is provided as well. Finally, with the assistance of these outcomes, we give a midpoint type inequality and some of its approximations for convex functions in symmetric quantum calculus.

Keywords

• hermite-hadamard inequality
• convex functions
• symmetric quantum calculus