Alp, NecmettinSarıkaya, Mehmet ZekiKunt, Mehmetİşcan, İmdat2020-04-302020-04-3020181018-36472213-686Xhttps://doi.org/10.1016/j.jksus.2016.09.007https://hdl.handle.net/20.500.12684/4291iscan, imdat/0000-0001-6749-0591; Kunt, Mehmet/0000-0002-8730-5370WOS: 000429915900008In this paper, we prove the correct q-Hermite-Hadamard inequality, some new q-Hermite-Hadamard inequalities, and generalized q-Hermite-Hadamard inequality. By using the left hand part of the correct q-Hermite-Hadamard inequality, we have a new equality. Finally using the new equality, we give some q-midpoint type integral inequalities through q-differentiable convex and q-differentiable quasi-convex functions. Many results given in this paper provide extensions of others given in previous works. (C) 2016 The Authors. Production and hosting by Elsevier B.V.en10.1016/j.jksus.2016.09.007info:eu-repo/semantics/openAccessHermite-Hadamard inequalityMidpoint type inequalityq-Integral inequalitiesq-Derivativeq-IntegrationConvexityQuasi-convexityArticle302193203WOS:000429915900008Q1Q2