## Generalized Ostrowski type inequalities for local fractional integrals

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- by Mehmet Zeki Sarikaya and Hüseyin Budak
- Proc. Amer. Math. Soc.
**145**(2017), 1527-1538 - 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 $R^{\alpha }$.## References

- M. Alomari, M. Darus, S. S. Dragomir, and P. Cerone,
*Ostrowski type inequalities for functions whose derivatives are $s$-convex in the second sense*, Appl. Math. Lett.**23**(2010), no. 9, 1071–1076. MR**2659140**, DOI 10.1016/j.aml.2010.04.038 - Mohammad W. Alomari, M. Emin Özdemir, and Havva Kavurmac,
*On companion of Ostrowski inequality for mappings whose first derivatives absolute value are convex with applications*, Miskolc Math. Notes**13**(2012), no. 2, 233–248. MR**3002626**, DOI 10.18514/mmn.2012.480 - M. W. Alomari and M. Darus,
*Some Ostrowski’s type inequalities for convex functions with application*, RGMIA Res. Rep. Coll. 13(1) 2010, Art. 3. - N. S. Barnett and S. S. Dragomir,
*An Ostrowski type inequality for double integrals and applications for cubature formulae*, Soochow J. Math.**27**(2001), no. 1, 1–10. MR**1821346** - Pietro Cerone and Sever S. Dragomir,
*Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions*, Demonstratio Math.**37**(2004), no. 2, 299–308. MR**2057852**, DOI 10.1515/dema-2004-0208 - S. S. Dragomir,
*Ostrowski type inequalities for functions whose derivatives are h-convex in absolute value*, RGMIA Research Report Collection, 16(2013), Article 71, 15 pp. - Sever S. Dragomir,
*Ostrowski type inequalities for functions whose derivatives are $h$-convex in absolute value*, Tbilisi Math. J.**7**(2014), no. 1, 1–17. MR**3313040**, DOI 10.2478/tmj-2014-0001 - S. S. Dragomir and R. P. Agarwal,
*Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula*, Appl. Math. Lett.**11**(1998), no. 5, 91–95. MR**1638774**, DOI 10.1016/S0893-9659(98)00086-X - U. S. Kirmaci and M. E. Özdemir,
*On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula*, Appl. Math. Comput.**153**(2004), no. 2, 361–368. MR**2064663**, DOI 10.1016/S0096-3003(03)00637-4 - Uǧur S. Kirmaci,
*Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula*, Appl. Math. Comput.**147**(2004), no. 1, 137–146. MR**2007685**, DOI 10.1016/S0096-3003(02)00657-4 - Huixia Mo, Xin Sui, and Dongyan Yu,
*Generalized convex functions on fractal sets and two related inequalities*, Abstr. Appl. Anal. , posted on (2014), Art. ID 636751, 7. MR**3226218**, DOI 10.1155/2014/636751 - Alexander Ostrowski,
*Über die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert*, Comment. Math. Helv.**10**(1937), no. 1, 226–227 (German). MR**1509574**, DOI 10.1007/BF01214290 - M. Emin Özdemir, Havva Kavurmacı, and Merve Avcı,
*Ostrowski type inequalities for convex functions*, Tamkang J. Math.**45**(2014), no. 4, 335–340. MR**3302307**, DOI 10.5556/j.tkjm.45.2014.1143 - Josip E. Pečarić, Frank Proschan, and Y. L. Tong,
*Convex functions, partial orderings, and statistical applications*, Mathematics in Science and Engineering, vol. 187, Academic Press, Inc., Boston, MA, 1992. MR**1162312** - M. Z. Sarikaya,
*On the Ostrowski type integral inequality*, Acta Math. Univ. Comenian. (N.S.)**79**(2010), no. 1, 129–134. MR**2684215** - Mehmet Zeki Sarikaya,
*On the Ostrowski type integral inequality for double integrals*, Demonstratio Math.**45**(2012), no. 3, 533–540. MR**2987183** - Mehmet Zeki Sarikaya and Hasan Ogunmez,
*On the weighted Ostrowski-type integral inequality for double integrals*, Arab. J. Sci. Eng.**36**(2011), no. 6, 1153–1160 (English, with English and Arabic summaries). MR**2845540**, DOI 10.1007/s13369-011-0102-4 - Mehmet Zeki Sarıkaya, Erhan. Set, M. Emin Ozdemir, and Sever S. Dragomir,
*New some Hadamard’s type inequalities for co-ordinated convex functions*, Tamsui Oxf. J. Inf. Math. Sci.**28**(2012), no. 2, 137–152. MR**3087182** - M. Z. Sarikaya and H. Yaldiz,
*On the Hadamard’s type inequalities for*$L$*-Lipschitzian mapping*, Konuralp Journal of Mathematics, Volume 1, No. 2, pp. 33-40 (2013) - X. J. Yang,
*Advanced Local Fractional Calculus and Its Applications*, World Science Publisher, New York, 2012. - Yong-Ju Yang, Dumitru Baleanu, and Xiao-Jun Yang,
*Analysis of fractal wave equations by local fractional Fourier series method*, Adv. Math. Phys. , posted on (2013), Art. ID 632309, 6. MR**3071601**, DOI 10.1155/2013/632309

## Bibliographic Information

**Mehmet Zeki Sarikaya**- Affiliation: Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
- MR Author ID: 690360
- Email: sarikayamz@gmail.com
**Hüseyin Budak**- Affiliation: Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
- MR Author ID: 1094290
- Email: hsyn.budak@gmail.com
- Received by editor(s): June 18, 2015
- Published electronically: December 27, 2016
- Communicated by: Ken Ono
- © Copyright 2016 American Mathematical Society
- 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
- MathSciNet review: 3601545