Some new fractional integral inequalities for \(s\)-convex functions

Volume 10, Issue 9, pp 4552--4563 http://dx.doi.org/10.22436/jnsa.010.09.01

Publication Date: September 06, 2017 Submission Date: June 21, 2017

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Authors

Dunya Karapinar - Department of Mathematics, Faculty of Sciences, Karadeniz Technical University, Trabzon 61080, Turkey. Sercan Turhan - Department of Mathematics, Faculty of Sciences and Arts, Giresun University, Giresun 28200, Turkey. Mehmet Kunt - Department of Mathematics, Faculty of Sciences, Karadeniz Technical University, Trabzon 61080, Turkey. Imdat Iscan - Department of Mathematics, Faculty of Sciences and Arts, Giresun University, Giresun 28200, Turkey.

Abstract

In this paper, a similar equality which is given in [C. Yildiz, M. E.Ozdemir, M. Z. Sarikaya, Kyungpook Math. J., \({\bf 56}\) (2016), 161--172] is proved by using different symbols and impressions. By using this equality, some new fractional integral inequalities for \(s\)-convex functions are obtained. Also, some applications to special means of positive real numbers are given. If the \(\alpha=1\) is taken, our results coincide with the results given in [E. Set, M. E. Ozdemir, M. Z. Sarikaya, Facta Unv. Ser. Math. Inform., \({\bf 27}\) (2012), 67--82]\) so our results are more general from the results given there.

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Keywords

• Ostrowski type inequalities
• midpoint type inequalities
• Riemann-Liouville fractional integrals
• s-convex functions.

MSC

•  26A51
•  26A33
•  26D10

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