New Generalizations of Ostrowski-Like Type Inequalities for Fractional Integrals

• Journal title : Kyungpook mathematical journal
• Volume 56, Issue 1,  2016, pp.161-172
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2016.56.1.161
Title & Authors
New Generalizations of Ostrowski-Like Type Inequalities for Fractional Integrals
Yildiz, Cetin; Ozdemir, Muhamet Emin; Sarikaya, Mehmet Zeki;

Abstract
In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality.
Keywords
Ostrowski`s Inequality;Convex(Concave) Functions;Riemann-Liouville Fractional Integration;$\small{H{{\ddot{o}}older}$ Inequality;Power-mean Inequality;
Language
English
Cited by
References
1.
A. M. Ostrowski, Uber die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv., 10(1938), 226-227.

2.
S. S. Dragomir, The Ostrowski integral inequality for Lipschitzian mappings and applications, Comput. Math. Appl., 38 (1999), 33-37.

3.
Z. Liu, Some companions of an Ostrowski type inequality and application, J. Inequal. in Pure and Appl. Math., 10(2), 2009, Art. 52, 12 pp.

4.
B. G. Pachpatte, On an inequality of Ostrowski type in three independent variables, J. Math.Anal. Appl., 249(2000), 583-591.

5.
B. G. Pachpatte, On a new Ostrowski type inequality in two independent variables, Tamkang J. Math., 32(1)(2001), 45-49

6.
M. Alomari, M. Darus, Some Ostrowski type inequalities for convex functions with applications, RGMIA 13(1)(2010) article No. 3. Preprint..

7.
M. Alomari, M. Darus, S. S. Dragomir, P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Appl. Math. Lett., 23(2010), 1071-1076.

8.
M. Z. Sarikaya, On the Ostrowski type integral inequality, Acta Math. Univ. Comenianae, Vol. LXXIX, 1(2010), pp. 129-134

9.
M. Z. Sarikaya, E. Set, H. Yaldiz and N. Basak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. and Comput. Mod., 57(9-10)(2013), 2403-2407.

10.
M. Z. Sarikaya, H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, Abstract and Applied Analysis, 2012.

11.
C. Yildiz, M. E. Ozdemir and H. K. Onalan, Fractional integral inequalities for different functions, New Trends in Mathematical Sciences, 3(2)2015, 110-117.

12.
E. Set, New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals, Comput. Math. Appl., 63(7)(2012), 1147-1154.

13.
B. Belarbi, Z. Dahmani, On some new fractional integral inequalities, J. Ineq. Pure and Appl. Math., 10(3)(2009), Art. 86.

14.
Z. Dahmani, New inequalities in fractional integrals, International Journal of Nonlinear Science, 9(4)(2010), 493-497.

15.
Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(1)(2010), 51-58.

16.
Z. Dahmani, L. Tabharit and S. Taf, Some fractional integral inequalities, Nonl. Sci. Lett. A., 1(2)(2010), 155-160.

17.
Z. Dahmani, L. Tabharit and S. Taf, New generalizations of Gruss inequality using Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl., 2(3)(2010), 93-99.

18.
S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives Theory and Application, Gordan and Breach Science, New York, 1993.