Hermite-Hadamard and Ostrowski type inequalities in $\mathfrak{h}$-calculus with applications

In this paper, we prove Hermite-Hadamard inequality for convex functions in the framework of $\mathfrak{h}$-calculus. We also use the notions of $\mathfrak{h}$-derivative and $\mathfrak{h}$-integral to prove Ostrowski's and trapezoidal type inequalities for bounded functions. It is also shown that the newly established inequalities are the generalization of the comparable inequalities in the literature. Finally, using some examples, we demonstrate the validity of newly formed inequalities and show how they can be used to special means of real numbers.