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

Advances in Difference Equations

article

Budak, Hüseyin¹  Hezenci, Fatih¹  Kara, Hasan¹ 

[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

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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$\mathbb{R} ^{2}$ . 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】

CC BY