$ (m, n) $-Harmonically polynomial convex functions and some Hadamard type inequalities on the co-ordinates

Abstract

In this study, we have introduced a new concept called $ (m, n) $-harmonically polynomial convex functions on the co-ordinates. Then, we have demonstrated some properties of this definition. Based on the definition and some elementary analysis process, we have proved a new Hadamard type integral inequality on the coordinates for $ (m, n) $-harmonically polynomial convex functions. Finally, we have established Hadamard type inequality for differentiable $ (m, n) $-Harmonically polynomial convex functions. We have also given some special cases for bounded functions.