Generalized Midpoint Type Inequalities Within the (p,q) -Calculus Framework

A novel (p,q) -montgomery identity is hereby established. Using this identity, we obtain some quantum midpoint type inequalities via strongly preinvex functions of higher-order σ >0 with respect to μ >0 . Our results complement, generalize and extend the results in the paper (Kunt et al. in RACSAM 112:969–992, 2018) and other related results in this research area. By choosing different values of μ , loads of interesting inequalities can be deduced. Besides these, we added to the literature a new version of the (p,q) -Ostrowski inequality. We hope that the findings of this paper will find their place in the field of convex and numerical analysis.