Fractional Ostrowski type inequalities for functions whose modulus of the first derivatives are prequasi-invex

• Autorzy: Meftah Badreddine

Identyfikatory

DOI

10.1515/jaa-2019-0017

• Języki publikacji: EN

Abstrakty

EN

In this paper, we establish fractional Ostrowski inequalities for functions whose modulus of the first derivatives are prequasi-invex. Midpoint inequalities are also derived.

Słowa kluczowe

EN

Ostrowski inequality; midpoint inequality; Hölder inequality

PL

nierówność Ostrowskiego; nierówność środkowa; nierówność Höldera

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2019
• Tom: Vol. 25, nr 2
• Strony: 165--171
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Meftah Badreddine

• Department of Mathematics, Faculté des Sciences et de la Technologie, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria

Bibliografia

• [1] M. Alomari and M. Darus, Some Ostrowski type inequalities for quasi-convex functions with applications to special means, RGMIA 13 (2010), no. 2, Article No. 3.
• [2] M. W. Alomari and S. Hussain, An inequality of Ostrowski’s type for preinvex functions with applications, Tamsui Oxf. J. Inf. Math. Sci. 29 (2013), no. 1, 29-37.
• [3] T. Antczak, Mean value in invexity analysis, Nonlinear Anal. 60 (2005), no. 8, 1473-1484.
• [4] N. S. Barnett, P. Cerone, S. S. Dragomir, M. R. Pinheiro and A. Sofo, Ostrowski type inequalities for functions whose modulus of the derivatives are convex and applications, in: Inequality Theory and Applications. Vol. 2 (Chinju/Masan 2001), Nova Science, Hauppauge (2003), 19-32.
• [5] H. Budak and M. Z. Sarikaya, On generalized Ostrowski-type inequalities for functions whose first derivatives absolute values are convex, Turkish J. Math. 40 (2016), no. 6, 1193-1210.
• [6] P. Cerone and S. S. Dragomir, Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions, Demonstr. Math. 37 (2004), no. 2, 299-308.
• [7] S. S. Dragomir and C. E. M. Pearce, Quasi-convex functions and Hadamard’s inequality, Bull. Aust. Math. Soc. 57 (1998), no. 3, 377-385.
• [8] S. S. Dragomir and A. Sofo, Ostrowski type inequalities for functions whose derivatives are convex, RGMIA Res. Rep. Coll. 5 (2002), Supplement Article 30, Proceedings of the 4th International Conference on Modelling and Simulation (Victoria University, Melbourne, Australia/November 11-13, 2002).
• [9] M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80 (1981), no. 2, 545-550.
• [10] I. Işcan, Ostrowski type inequalities for functions whose derivatives are preinvex, Bull. Iranian Math. Soc. 40 (2014), no. 2, 373-386.
• [11] D. A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, An. Univ. Craiova Ser. Mat. Inform. 34 (2007), 83-88.
• [12] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006.
• [13] B. Meftah, Ostrowski inequalities for functions whose first derivatives are logarithmically preinvex, Chin. J. Math. (N.Y.) 2016 (2016), Article ID 5292603.
• [14] B. Meftah, Some new Ostrwoski’s inequalities for functions whose nth derivatives are r-convex, Int. J. Anal. 2016 (2016), Article ID 6749213.
• [15] D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Classical and New Inequalities in Analysis, Math. Appl. (East European Ser.) 61, Kluwer Academic, Dordrecht, 1993.
• [16] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Math. Sci. Eng. 187, Academic Press, Boston, 1992.
• [17] R. Pini, Invexity and generalized convexity, Optimization 22 (1991), no. 4, 513-525.
• [18] M. Z. Sarikaya and H. Budak, Generalized Ostrowski type inequalities for local fractional integrals, Proc. Amer. Math. Soc. 145 (2017), no. 4, 1527-1538.
• [19] M. Z. Sarikaya, S. Erden and H. Budak, Some generalized Ostrowski type inequalities involving local fractional integrals and applications, Adv. Inequal. Appl. 2016 (2016), Article ID 6.
• [20] 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 (2012), no. 7, 1147-1154.
• [21] K.-L. Tseng, Improvements of some inequalities of Ostrowski type and their applications, Taiwanese J. Math. 12 (2008), no. 9, 2427-2441.
• [22] T. Weir and B. Mond, Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl. 136 (1988), no. 1, 29-38.
• [23] H. Yue, Ostrowski inequality for fractional integrals and related fractional inequalities, Transylv. J. Math. Mech. 5 (2013), no. 1, 85-89.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).