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

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 th...

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Veröffentlicht in:Advances in difference equations 2021-06, Vol.2021 (1), p.1-32, Article 312
Hauptverfasser: Budak, Hüseyin, Hezenci, Fatih, Kara, Hasan
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Sprache:eng
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Zusammenfassung: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 . 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.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03463-0