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Abstrakty
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.
Czasopismo
Rocznik
Tom
Strony
5--27
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Department of Mathematics, Texas A&M University, Kingsville, TX 78363-8202, USA
autor
- Department of Mathematics, East China Normal University, Shanghai 200241, People's Republic of China
autor
- 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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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