Alp, NecmettinBudak, HuseyinSarikaya, Mehmet ZekiAli, Muhammad Aamir2024-08-232024-08-2320240035-75961945-3795https://doi.org/10.1216/rmj.2024.54.361https://hdl.handle.net/20.500.12684/14039We aim to prove generalized estimations for the q-Hermite-Hadamard inequality for convex functions using a parameter. By choosing this particular parameter, we show that our results reduce the previously obtained q-Hermite-Hadamard inequalities. We also present some new refinements of these q-Hermite- Hadamard inequalities. Furthermore, we establish a new lemma and, by using this lemma, we obtain some new quantum inequalities that generalize quantum midpoint and quantum trapezoid inequalities for convex functions.en10.1216/rmj.2024.54.361info:eu-repo/semantics/closedAccessq-derivativeq-integral inequalitiesquantum calculusconvexityMidpoint Type InequalitiesIntegral-InequalitiesArticle5423613742-s2.0-85193721748WOS:001235100700022Q2N/A