Fractional Ostrowski Inequalities for s-Godunova-Levin Functions

Noor, Muhammad Aslam; Noor, Khalida Inayat; Awan, Muhammad Uzair

Research Article

Fractional Ostrowski Inequalities for s-Godunova-Levin Functions

Muhammad Aslam Noor
Khalida Inayat Noor
Muhammad Uzair Awan¹*

CIIT, Islamabad, Pakistan.

* Corresponding author

Abstract

In this paper, we derive some new fractional Ostrowski type inequalities for s-Godunova-Levin functions introduced by Dragomir [3, 4]. Some special cases are also discussed.

How to Cite

M. A. Noor, K. I. Noor, M. U. Awan, Fractional Ostrowski Inequalities for s-Godunova-Levin Functions, Int. J. Anal. Appl. 5 (2014), 167–173.

BibTeX

@article{Noor2014,
  author  = {Noor, Muhammad Aslam and Noor, Khalida Inayat and Awan, Muhammad Uzair},
  title   = {Fractional Ostrowski Inequalities for s-Godunova-Levin Functions},
  journal = {Int. J. Anal. Appl.},
  volume  = {5},
  year    = {2014},
  pages   = {167--173},
  doi     = {}
}

References

[1] G. Cristescu, L. Lupsa, Non-connected Convexities and Applications, Kluwer Academic Publishers, Dordrecht, Holland, 2002.
[2] G. Cristescu, M. A. Noor, M. U. Awan, Bounds of the second degree cumulative frontier gaps of functions with generalized convexity, Carpath. J. Math. 30(2), 2014.
[3] S. S. Dragomir, Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, preprint.
[4] S. S. Dragomir, n-points inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, preprint.
[5] S. S. Dragomir, R. P. Agarwal, P. Cerone, On Simpsons Inequality and Applications, J. Inequal. Appl., 5, 533-579, 2000.
[6] S. S. Dragomir, J. Peˇcari ´c and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math, 21 (1995), 335-341.
[7] S. S. Dragomir, C. E. M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, Victoria University, Australia 2000.
[8] S. S. Dragomir, T. M. Rassias, Ostrowski Type Inequalities and Applications in Numerical Integration, Springer Netherlands, 2002.
[9] E. K. Godunova and V. I. Levin, Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions. (Russian) Numerical mathematics and mathematical physics (Russian), 138-142, 166, Moskov. Gos. Ped. Inst., Moscow, 1985.
[10] U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput. 218(3), 860-865 (2011).
[11] A. Kilbas , H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier B.V., Amsterdam, Netherlands, (2006).
[12] W. Liu, J. Park, A generalization of the companion of Ostrowski-like inequality and applications, Appl. Math. Inf. Sci. 7(1), 273-278 (2013).
[13] D. S. Mitrinovic, J. Pecaric, Note on a class of functions of Godunova and Levin, C. R. Math. Rep. Acad. Sci. Can. 12, 33-36, (1990).
[14] M. A. Noor, M. U. Awan, Some Integral inequalities for two kinds of convexities via fractional integrals, Trans. J. Math. Mech., 5(2), (2013).
[15] M. A. Noor, K. I. Noor, M. U. Awan, Geometrically relative convex functions, Appl. Math. Infor. Sci. 8(2), 607-616, (2014).
[16] M. A. Noor, K. I. Noor, M. U. Awan, S. Khan, Fractional Hermite-Hadamard Inequalities for some new classes of Godunova-Levin functions, Appl. Math. Infor. Sci. (2014/15), inpress.
[17] M. A. Noor, K. I. Noor, M. U. Awan, J. Li, On Hermite-Hadamard Inequalities for h-preinvex functions, Filomat, (2014), inpress.
[18] M. A. Noor, F. Qi, M. U. Awan, Some HermiteHadamard type inequalities for log -h-convex functions, Analysis, 33, 367?75, (2013).
[19] A. Ostrowski, Uber die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert, Comment. Math. Hel, 10 (1938), 226-227.
[20] M. Radulescu. S. Radulescu, P. Alexandrescu, On the Godunova-Levin-Schur class of functions, Math. Inequal. Appl. 12(4), 853-862, (2009).
[21] M. Z. Sarikaya, E. Set, H. Yaldiz and N. Basak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling 57 (2013), 2403-2407.
[22] 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?154.
[23] M. Tunc, Ostrowski-type inequalities via h-convex functions with applications to speial means, J. Ineq. Appl. 2013,2013:326, doi:10.1186/1029-242X-2013-326.
[24] Y Wang, S.-H Wang, F. Qi, Simpson type integral inequalities in which the power of the absolute value of the first derivative of the integrand is s-preinvex, Acta Universities (NIS) Ser. Math. Inform. 28, 1-9, (2013).
[25] B.-Y Xi, F. Qi, Integral inequalities of simpson type for logarithmically convex functions, To appear in Advanced Studies in Contemporary Mathematics.