Midpoint Inequalities in Fractional Calculus Defined Using Positive Weighted Symmetry Function Kernels
Pshtiwan Othman Mohammed, Hassen Aydi, Artion Kashuri, Y. S. Hamed, Khadijah M. Abualnaja
Abstract
The aim of our study is to establish, for convex functions on an interval, a midpoint version of the fractional HHF type inequality. The corresponding fractional integral has a symmetric weight function composed with an increasing function as integral kernel. We also consider a midpoint identity and establish some related inequalities based on this identity. Some special cases can be considered from our main results. These results confirm the generality of our attempt.
Topics & Concepts
MidpointMathematicsRegular polygonFractional calculusWeight functionConvex functionIdentity (music)Interval (graph theory)Function (biology)Pure mathematicsSymmetry (geometry)Kernel (algebra)Monotonic functionCalculus (dental)Mathematical analysisApplied mathematicsCombinatoricsGeometryMedicineAcousticsEvolutionary biologyBiologyDentistryPhysicsMathematical Inequalities and ApplicationsProbabilistic and Robust Engineering DesignFunctional Equations Stability Results