In this research, for interval-valued functions, we give a new version of Jensen inclusion which is called Jensen-Mercer inclusion. Moreover, we establish some new inclusions of Hermite-Hadamard-Mercer type for interval-valued functions.

In this note, for differentiable convex functions, we prove some new Ostrowski-Mercer inequalities. These inequalities generalize an Ostrowski inequality and related inequalities proved in [3,5]. Some applications to special means are also given.

In this study, we give the notions about some new post-quantum partial derivatives and then use these derivatives to prove an integral equality via post-quantum double integrals. We establish some new post-quantum Ostrowski type inequalities for differentiable coordinated functions using the newly established equality. We also show that the results presented in this paper are the extensions of some existing results.