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

Advances in Difference Equations

Hüseyin Budak¹  Fatih Hezenci¹  Hasan Kara¹ 

[1] Department of Mathematics, Faculty of Science and Arts, Düzce University;

关键词: Simpson inequality;    Ostrowski inequality;    Co-ordinated convex function;    Generalized fractional integrals;   

DOI  :  10.1186/s13662-021-03463-0

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown