Saowaluck ChasreechaiMuhammad Aamir AliMuhammad Amir AshrafThanin SitthiwiratthamSina EtemadManuel De la SenShahram Rezapour2025-03-102025-03-102023Axioms2075168010.3390/axioms120100492-s2.0-85146743539https://repository.dusit.ac.th//handle/123456789/4575In this paper, we first establish two quantum integral (q-integral) identities with the help of derivatives and integrals of the quantum types. Then, we prove some new q-midpoint and q-trapezoidal estimates for the newly established q-Hermite-Hadamard inequality (involving left and right integrals proved by Bermudo et al.) under q-differentiable convex functions. Finally, we provide some examples to illustrate the validity of newly obtained quantum inequalities. © 2023 by the authors.All Open Access; Gold Open Access; Green Open Accessconvex functionHermite-Hadamard inequalityq-integralquantum calculusArticleScopus