Thanin SitthiwiratthamMuhammad Aamir AliHŸseyin BudakSina EtemadShahram Rezapour2025-03-102025-03-102022Boundary Value Problems1687276210.1186/s13661-022-01665-32-s2.0-85141630503https://repository.dusit.ac.th//handle/123456789/4620In this paper, we conduct a research on a new version of the (p, q) -HermiteÐHadamard inequality for convex functions in the framework of postquantum calculus. Moreover, we derive several estimates for (p, q) -midpoint and (p, q) -trapezoidal inequalities for special (p, q) -differentiable functions by using the notions of left and right (p, q) -derivatives. Our newly obtained inequalities are extensions of some existing inequalities in other studies. Lastly, we consider some mathematical examples for some (p, q) -functions to confirm the correctness of newly established results. © 2022, The Author(s).All Open Access; Gold Open Access(p, q) -calculus(p, q) -HermiteÐHadamard inequalityConvex functionsq-calculusArticleScopus