# Some new fractional integral inequalities for $s$-convex functions

Volume 10, Issue 9, pp 4552--4563 Publication Date: September 06, 2017       Article History
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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.

### Keywords

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

•  26A51
•  26A33
•  26D10

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