Butt, Saad IhsanUmar, MuhammadBudak, Hüseyin2024-08-232024-08-2320232073-8994https://doi.org/10.3390/sym15051038https://hdl.handle.net/20.500.12684/13802The objective of this study is to identify novel quantum midpoint-type inequalities for twice q-differentiable functions by utilizing Mercer's approach. We introduce a new auxiliary variant of the quantum Mercer midpoint-type identity related to twice q-differentiable functions. By applying the theory of convex functions to this identity, we introduce new bounds using well-known inequalities, such as Holder's inequality and power-mean inequality. We provide explicit examples along with graphical demonstrations. The findings of this study explain previous studies on midpoint-type inequalities. Analytic inequalities of this type, as well as related strategies, have applications in various fields where symmetry plays an important role.en10.3390/sym15051038info:eu-repo/semantics/openAccessquantum calculusconvex functionsmidpoint inequalitiesJensen-Mercer inequalityRefinementsConvexArticle1552-s2.0-85160545213WOS:000997794300001Q2Q2