Litcius/Paper detail

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

Hüseyin Budak, Fatih Hezenci, Hasan Kara

2021Advances in Difference Equations49 citationsDOIOpen Access PDF

Abstract

Abstract In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane $\mathbb{R} ^{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>R</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math> . Furthermore, by special choice of parameters in our main results, we obtain several well-known inequalities such as the Ostrowski inequality, trapezoidal inequality, and the Simpson inequality for Riemann and Riemann–Liouville fractional integrals.

Topics & Concepts

MathematicsDifferentiable functionConvex functionType (biology)Mathematical analysisRegular polygonFractional calculusPure mathematicsComplex planeIdentity (music)GeometryPhysicsBiologyAcousticsEcologyMathematical Inequalities and ApplicationsFunctional Equations Stability Results
On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals | Litcius