q-Hermite-Hadamard Integral Inequality for the Coordinated Convex Functions

Abstract

The calculus without the notion of limits is quantum calculus. Its study dates back to L. Euler in the middle of the eighteenth century whereas the systematic initiation on it was done by F.H. Jackson in the beginning of the twentieth century. The rapid growth on q-calculus is due to its applications in various branches of mathematical and physical sciences. Of them, one of the most basic and important functions in the theory of geometric function is convexity having its wider applications in pure and applied mathematics. As it still lacks the intensive study on quantum estimates on the various types of integral inequalities, we focus our study on quantum estimates of Hermite-Hadamard type integral  inequality especially on coordinated convex functions. In this paper, we have extended Hermite-Hadamard type integral inequality for coordinated convex function in terms of quantum framework.