Ostrowski-type fractional integral inequalities for mappings whose derivatives are h-convex via Katugampola fractional integrals
DOI:
https://doi.org/10.24193/subbmath.2018.4.04Keywords:
Ostrowski inequality, fractional integrals, convex functions, h-Convex functions.Abstract
In this paper we generalize some Riemann-Liouville fractional integral inequalities of Ostrowski-type for h-convex functions via Katugampola fractional integrals, generalizations of the Riemann-Liouville and the Hadamard fractional integrals. Also we deduce some known results by using p-functions, convex functions and s-convex functions.
Mathematics Subject Classification (2010): 26A33, 26A51, 26D07, 26D10, 26D15.
References
Dragomir, S.S., Ostrowski-type inequalities for Lebesgue integral: A survey of recent results, Aust. J. Math. Anal. Appl., 14(2017), no. 1, 1-287.
Dragomir, S.S., Peˇcari´c, J., Persson, L.E., Some inequalities of Hadamard type, Soochow J. Math., 21(1995), 335-341.
Farid, G., Some new Ostrowski-type inequalities via fractional integrals, Int. J. Anal. App., 14(2017), no. 1, 64-68.
Farid, G., Katugampola, U.N., Usman, M., Ostrowski-type fractional integral inequalities for S-Godunova-Levin functions via Katugampola fractional integrals, Open J. Math. Sci., 1(2017), no. 1, 97–110.
Farid, G., Rafique, S., Rehman, A. Ur., More on Ostrowski and Ostrowski-Gruss type inequalities, Commun. Optim. Theory, 2017(2017), ArtID 15, 9 pages.
Farid, G., Usman, M., Ostrowski-type k-fractional integral inequalities for MT-convex and h-convex functions, Nonlinear Funct. Anal. Appl., 22(2017), no. 3, 627-639.
Godunova, E.K., Levin, V.I., Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions, Numerical Mathematics and Mathe- matical Physics (Russian), Moskov. Gos. Ped. Inst. Moscow, (1985), 138-142.
Hadamard, J., Essai sur l’etude des fonctions donnees par leur developpment de Taylor, Journal de Math´ematiques Pures et Appliqu´ees, 8(1892), 101–186.
Holmgren, H.J., Om differentialkalkylen med indices of hvad nature sam heist, Kongliga Svenska Vetenskaps-Akademiens Handlinger, 5(1865-1866), no. 11, 1-83.
Hudzik, H., Maligranda, L., Some remarks on s-convex functions, Aequationes Math., 48(1994), 100–111.
Katugampola, U.N., New approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6(2014), no. 4, 1–15.
Laurent, H., Sur le calcul des derivees a indicies quelconques, Nouv. Annales de Mathematik, 3(1884), no. 3, 240–252.
Letnikov, A.V., An explanation of the concepts of the theory of differentiation with arbitrary index, Moscow Matem. Sbornik, 6(1872), 413–445.
Liu, W., Ostrowski-type fractional integral inequalities for MT-convex function, Miskole Mathematical Notes, 16(2015), no. 1, 249–256.
Matloka, M., Ostrowski-type inequalities for functions whose derivatives are h-convex via fractional integrals, Journal of Scientific Research and Reports, 3(12)(2014), Article No. JSRR.2014.12.005, 1633–1641.
Mitrinovi´c, D.S., Peˇcari´c, J., Fink, A.M., Inequalities involving functions and their integrals and derivatives, Kluwer Academic Publisher Group, Dordrecht, 53(1991).
Ostrowski, A., Uber die Absolutabweichung einer differentierbaren funktion von ihrem integralmittelwert, Comment. Math. Helv., 10(1938), no. 1, 226–227.
Sonin, N. Ya., On differentiation with arbitrary index, Moscow Matem. Sbornik, 6(1869), no. 1, 1–38.
Varosanec, S., On h-convexity, J. Math. Anal. Appl., 326(2007), no. 1, 303–311.
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