On Ostrowski type inequalities

• Autorzy: Agarwal R. P. , Luo M.-J. , Raina R. K.

Identyfikatory

DOI

10.1515/fascmath-2016-0001

• Języki publikacji: EN

Abstrakty

EN

In this paper, new forms of Ostrowski type inequalities are established for a general class of fractional integral operators. The main results are used to derive Ostrowski type inequalities involving the familiar Riemann-Liouville fractional integral operators and other important integral operators. We further obtain similar types of inequalities for the integral operators whose kernels are the Fox-Wright generalized hypergeometric function. Several consequences and special cases of some of the results including applications to Stolarsky's means are also pointed out.

Słowa kluczowe

EN

Ostrowski's inequality; s-convex functions; Riemann-Liouville fractional integral operator; Fox-Wright function; Stolarsky's means

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2016
• Tom: Nr 56
• Strony: 5--27
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Agarwal R. P.

• Department of Mathematics, Texas A&M University, Kingsville, TX 78363-8202, USA

autor

Luo M.-J.

• Department of Mathematics, East China Normal University, Shanghai 200241, People's Republic of China

autor

Raina R. K.

• M.P. University of Agriculture and Technology, Udaipur-313002, Rajasthan, India

Bibliografia

• [1] Alomari M., Darus M., Dragomir S.S., Cerone P., Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Appl. Math. Lett., 23(2010), 1071-1076.
• [2] Anastassiou G.A., Ostrowski type inequalities, Proc. Amer. Math. Soc., 123 (1995), 3775-3781.
• [3] Borwein J.M., Borwein P.B., The way of all means, Amer. Math. Monthly, 94(1987), 519-522.
• [4] Dragomir S.S., Operator Inequalities of Ostrowski and Trapezoidal Type, Springer Briefs in Mathematics, Springer, New York, 2012. x+112 pp. ISBN: 978-1-4614-1778-1.
• [5] Katugampola U.N., New approach to a generalized fractional integral, Appl. Math. Comput., 218(2011), 860-865.
• [6] Kilbas A.A., Fractional calculus of the generalized Wright function, Fract. Calc. Appl. Anal., 8(2005), 113-126.
• [7] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V, Amsterdam, 2006.
• [8] Milovanović G.V., On some integral inequalities, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 498-541(1975), 119-124.
• [9] Milovanović G.V., Pečarić J.E., On generalization of the inequality of A. Ostrowski and some related applications, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 544-576(1976), 155-158.
• [10] Ostrowski A., Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv., 10(1938), 226-227.
• [11] Raina R.K., On generalized Wright's hypergeometric functions and fractional calculus operators, East Asian Math. J., 21(2)(2005), 191-203.
• [12] Sarikaya M.Z., Filiz H., Note on the Ostrowski type inequalities for fractional integrals, Vietnam J. Math., 42(2014), 187-190.
• [13] Sarikaya M.Z., Ogunmez H., On new inequalities via Riemann-Liouville fractional integration, Abstr. Appl. Anal., 2012, Article ID 428983.
• [14] Set E., New inequalities of Ostrowski type for mapping whose derivatives are s-convex in the second sense via fractional integrals, Comput. Math. Appl., 63(2012), 1147-1154.
• [15] Shukla A.K., Prajapati J.C., On a generalization of Mittag-Leffler function and its properties, J. Math. Anal. Appl., 336(2007), 797-811.
• [16] Srivastava H.M., Tomovski Ž. Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Appl. Math. Comput., 211(2009), 198-210.
• [17] Stolarsky K.B., Generalizations of the logarithmic mean, Math. Mag., 48 (1975), 87-92.
• [18] Tomovski Ž., Hilfer R., Srivastava H.M., Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions, Integral Transforms Spec. Funct., 21(2010), 797-814.
• [19] Wang M., A probabilistic version of Ostrowski inequality, Appl. Math. Lett., 24(2011), 270-274.
• [20] Yildirim H., Kirtay Z., Ostrowski inequality for generalized fractional integral and related inequalities, Malaya J. Mat., 2(3)(2014), 322-329.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.