$ (m, n) $-Harmonically polynomial convex functions and some Hadamard type inequalities on the co-ordinates
Saad Ihsan Butt, Ahmet Ocak Akdemi̇r, Muhammad Nadeem, Nabil Mlaiki, İşcan İmdat, Thabet Abdeljawad
Abstract
<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. </abstract>
Topics & Concepts
MathematicsDifferentiable functionHadamard transformPolynomialBounded functionConvex functionConvex analysisSubderivativeType (biology)Pure mathematicsRegular polygonConvex optimizationCombinatoricsMathematical analysisGeometryEcologyBiologyMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsNonlinear Differential Equations Analysis