Yildirim, Hüseyin; Yildirim, Seda Kilinç On generalized fractional integral inequalities of Ostrowski type. (English) Zbl 1485.26027 Acta Comment. Univ. Tartu. Math. 25, No. 1, 143-151 (2021). The authors derive and prove some new generalizations of Ostrowski inequality using the concept of generalized Riemann-Liouville fractional integrals. Some special cases of the results obtained which yielded earlier Ostrowski type inequalities in the literature are pointed out and well discussed. Reviewer: James Adedayo Oguntuase (Abeokuta) MSC: 26D10 Inequalities involving derivatives and differential and integral operators 26A33 Fractional derivatives and integrals 26D15 Inequalities for sums, series and integrals 41A55 Approximate quadratures Keywords:fractional integral; Ostrowski inequality; Korkine’s identity; Riemann-Liouville fractional integral × Cite Format Result Cite Review PDF Full Text: DOI References: [1] A. Akkurt, M. Esra Yıldırım, and H.Yıldırım, On some integral inequalities for (k, h)-Riemann-Lioville fractional integral, New Trends Math. Sci. 4(2) (2016), 138-146. [2] M. Alomari and M. Darus, Some Ostrowski type inequalities for convex functions with applications, RGMIA 13(1) (2010), Article 3, 13 pp. [3] S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, J. Inequal. Pure Appl. Math. 10(3) (2009), Article 86, 5 pp. · Zbl 1184.26011 [4] Z. Dahmani, L. Tabharit, and S. Taf, Some fractional integral inequalities, Nonlinear. Sci. Lett. A 1(2) (2010), 155-160. [5] S. S. Dragomir, On the Ostrowski’s integral inequality for mappings with bounded variation and applications, Math. Inequal. Appl. 1(2) (2001), 59-66. · Zbl 1016.26017 [6] G. Grüss,Über das Maximum des absoluten Betrages von 1 (x)dx, Math. Z. 39 (1935), 215-226. · JFM 60.0189.02 [7] Y. Hu, Ostrowski inequality for fractional integrals and related fractional inequalities, TJMM 5 (2013), 85-89. · Zbl 1292.26067 [8] H. Kalsoom, M. Idrees, A. Kashuri, M. Uzair Awan, and Y.-M. Chu, Some new (p1p2, q1q2)-estimates of Ostrowski-type integral inequalities via n-polynomials s-type convexity, AIMS Math. 5(6) (2020), 7122-7144. · Zbl 1484.26030 [9] U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput. 218(3) (2011), 860-865. · Zbl 1231.26008 [10] M. A. Khan, S. Begum, Y. Khurshid, and Y.-M. Chu, Ostrowski type inequalities involving conformable fractional integrals, J. Inequal. Appl. 2018, Paper No. 70, 14 pp. · Zbl 1497.26030 [11] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Frac-tional Diferential Equations, Elsevier B.V., Amsterdam, 2006. · Zbl 1092.45003 [12] A. N. Korkine, Sur une therome de M. Tchebychef, C.R. Acad. Sci. Paris 96 (1883), 316-327. · JFM 15.0224.01 [13] Z. Liu, Some companions of an Ostrowski type inequality and application, J. Inequal. Pure Appl. Math. 10(2) (2009), Article 52, 12 pp. · Zbl 1168.26310 [14] A. M. Ostrowski,Über die Absolutabweichung einer differentiebaren Function von ihrem integral Mittelwert, Comment. Math. Helv. 10 (1938), 226-227. · JFM 64.0209.01 [15] B. G. Pachpatte, On a new Ostrowski type inequality in two independent variables, Tamkang J. Math. 32(1) (2001), 45-49. · Zbl 0982.26013 [16] S. Rashid, M. A. Noor, K. I. Noor, and Y.-M. Chu, Ostrowski type inequalities in the sense of generalized K-fractional integral operator for exponentially convex functions, AIMS Math. 5(3) (2020), 2629-2645. · Zbl 1484.26038 [17] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993. · Zbl 0818.26003 [18] M. Z. Sarikaya, On the Ostrowski type integral inequality, Acta Math. Univ. Comenian, 79(1) (2010), 129-134. · Zbl 1212.26058 [19] M. Z. Sarikaya, Ostrowski type inequalities involving the right Caputo fractional derivatives belong to Lp, Facta Univ. Ser. Math. Inform. 27(2) (2012), 191-197. · Zbl 1299.26056 [20] M. Z. Sarikaya and H. Filiz, Note on the Ostrowski type inequalities for fractional integrals, Vietnam J, Math. 42(2) (2014), 187-190. · Zbl 1298.26026 [21] M. Z. Sarıkaya and H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, arXiv:1005.1167v1 [math.CA] 7 May 2010. [22] N. Ujevic, Sharp inequalities of Simpson type and Ostrowski type, Comput. Math. Appl. 48 (2004), 145-151. · Zbl 1063.41023 [23] H. Yildirim and Z. Kirtay, Ostrowski inequality for generalized fractional integral and related inequalities, Malaya J. Mat. 2(3) (2014), 322-329. · Zbl 1371.26041 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.