$(m,n)$-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.

Keywords

• hadamard-type inequality
• co-ordinates
• $ (m， n) $-harmonically polynomial convex functions