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

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 $\mathbb{R} ^{2}$ R 2 . 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.

A Note on Fractional Midpoint Type Inequalities for Co-ordinated (s1, s2)-Convex Functions

“…Here, 𝛷(𝑎, 𝑏, 𝑥; 𝑐, 𝑑, 𝑦) is defined as in Lemma 1, 𝐴 𝑖 , 𝑖 = 1, 2, 3, 4 are described as in (9) and 𝐵 𝑖 , 𝑖 = 1, 2, 3, 4 are defined as in (10).…”

“…These authors investigated Hermite-Hadamard inequalities for this kind of fractional integrals in [9]. For more information about these type of inequalities, we refer to [10][11][12].…”

Maclaurin-type inequalities for Riemann-Liouville fractional integrals

“…Budak et al [1] established some variants of Simpson-type inequalities for the case of differentiable convex functions and generalized fractional integrals. For further information concerned Simpson-type inequalities and some properties of Riemann-Liouville fractional integrals, the reader is referred to [2,16] and the references therein.…”

New generalizations of some important inequalities for Sarikaya fractional integrals

“…For further information about Simpson type inequalities for various convex classes, we refer the reader to Refs. [2,3,6,7,9,13,[17][18][19] and the references therein. Now, we introduce some definitions and notations which are used frequently in throughout main section.…”