Hermite–Hadamard integral inequalities on coordinated convex functions in quantum calculus
Manar A. Alqudah, Artion Kashuri, Pshtiwan Othman Mohammed, Thabet Abdeljawad, Muhammad Raees, Matloob Anwar, Y. S. Hamed
Abstract
Abstract At first, we recall the q -operators in the context of q -calculus and by examining these operators we will introduce new definitions of the partial q -operators. Then, we investigate some new refinements inequalities of Hermite–Hadamard ( $H-H$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> <mml:mo>−</mml:mo> <mml:mi>H</mml:mi> </mml:math> ) type on the coordinated convex functions involving the new defined partial q -operators. From our main results, we establish several specific inequalities and we point out the existing results which had already been obtained in the literature.
Topics & Concepts
MathematicsConvex functionHermite polynomialsContext (archaeology)Partial differential equationRegular polygonCalculus (dental)Pure mathematicsPartial derivativeAlgebra over a fieldMathematical analysisGeometryMedicinePaleontologyDentistryBiologyMathematical Inequalities and ApplicationsMathematical functions and polynomialsFunctional Equations Stability Results