Sitho, SurangAli, Muhammad AamirBudak, HuseyinNtouyas, Sotiris K.Tariboon, Jessada2021-12-012021-12-0120212227-7390https://doi.org/10.3390/math9141666https://hdl.handle.net/20.500.12684/10909In this article, we use quantum integrals to derive Hermite-Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We use the q(x)(2)- quantum integral to show midpoint and trapezoidal inequalities for q(x)(2)-differentiable preinvex functions. Furthermore, we demonstrate with an example that the previously proved Hermite- Hadamard-type inequality for preinvex functions via q(x)(1)-quantum integral is not valid for preinvex functions, and we present its proper form. We use q(x)(1)-quantum integrals to show midpoint inequalities for q(x)(1)-differentiable preinvex functions. It is also demonstrated that by considering the limit q -> 1(-) and eta(x(2), x(1)) = -eta(x(1), x(2)) = x(2), x(1) in the newly derived results, the newly proved findings can be turned into certain known results.en10.3390/math9141666info:eu-repo/semantics/openAccessHermite-Hadamard inequalityq-integralquantum calculuspreinvex functiontrapezoid inequalitiesmidpoint inequalitiesHermite-Hadamard InequalitiesIntegral-InequalitiesDifferentiable MappingsReal NumbersConvexArticle9142-s2.0-85111268366WOS:000677330600001Q2Q1