[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2016.56.1.161

New Generalizations of Ostrowski-Like Type Inequalities for Fractional Integrals

Yildiz, Cetin (Ataturk University, K. K. Education Faculty, Department of Mathematics)
Ozdemir, Muhamet Emin (Uludag University, Education Faculty, Department of Mathematics)
Sarikaya, Mehmet Zeki (Duzce University, Department of Mathematics, Faculty of Science and Arts)

Publication Information

Kyungpook Mathematical Journal / v.56, no.1, 2016 , pp. 161-172 More about this Journal

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; $H{{\ddot{o}}older$ Inequality; Power-mean Inequality;

Citations & Related Records

Reference

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. DOI
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. DOI
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. DOI
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. DOI
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. DOI
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.