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Generalized Ostrowski type inequalities for local fractional integrals


Authors: Mehmet Zeki Sarikaya and Hüseyin Budak
Journal: Proc. Amer. Math. Soc. 145 (2017), 1527-1538
MSC (2010): Primary 26D07, 26D10; Secondary 26D15, 26A33
DOI: https://doi.org/10.1090/proc/13488
Published electronically: December 27, 2016
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Abstract: First, we establish the generalized Ostrowski inequality for local fractional integrals on fractal sets $ R^{\alpha }$ $ \left ( 0<\alpha \leq 1\right ) $ of real line numbers. Secondly, we obtain some new inequalities using the generalized convex function on fractal sets $ R^{\alpha }$.


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Additional Information

Mehmet Zeki Sarikaya
Affiliation: Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
Email: sarikayamz@gmail.com

Hüseyin Budak
Affiliation: Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
Email: hsyn.budak@gmail.com

DOI: https://doi.org/10.1090/proc/13488
Keywords: Generalized Ostrowski inequality, generalized H\"older's inequality, generalized convex functions.
Received by editor(s): June 18, 2015
Published electronically: December 27, 2016
Communicated by: Ken Ono
Article copyright: © Copyright 2016 American Mathematical Society