Muhammad Aslam Noor, Khalida Inayat Noor, Muhammad Uzair Awan

DOI Number
First page
Last page


In this paper, we introduce some new classes of s-Godunova-Levin functions, which are called as sm-Godunova-Levin functions of first and second kinds. We show that these classes contains some previouslyknown classes of convex functions. Finally we establish some new Ostrowski inequalities for sm-Godunova-Levin functions via fractional integrals. Some special cases are also discussed.


Convex functions, s_m-Godunova-Levin functions, Ostrowski inequalities.

Full Text:



G. Cristescu, L. Lupsa, Non-connected Convexities and Applications, Kluwer Academic Publishers,

Dordrecht, Holland, 2002.

S. S. Dragomir, Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces,

preprint, (2014).

S. S. Dragomir, n-points inequalities of Hermite-Hadamard type for h-convex functions on linear

spaces, preprint, (2014).

S. S. Dragomir, J. Pecaric and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math,

(1995), 335-341.

S. S. Dragomir, C. E. M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications,

Victoria University, Australia 2000.

S. S. Dragomir, T. M. Rassias, Ostrowski Type Inequalities and Applications in Numerical Integration,

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.

U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput. 218(3),

-865 (2011).

W. Liu, J. Park, A generalization of the companion of Ostrowski-like inequality and applications,

Appl. Math. Inf. Sci. 7(1), 273-278 (2013).

V.G. Mihean, A generalization of the convexity, Seminar on Functional Equations, Approx. and

Convex., Cluj-Napoca, Romania, 1993.

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).

M. A. Noor, M. U. Awan, Some Integral inequalities for two kinds of convexities via fractional

integrals, Trans. J. Math. Mech., 5(2), (2013).

M. A. Noor, K. I. Noor, M. U. Awan, Geometrically relative convex functions, Appl. Math. Infor.

Sci. 8(2), 607-616, (2014).

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. Inf. Sci. 8, No. 6, 2865-2872 (2014).

A. Ostrowski, Uber die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmit-

telwert, Comment. Math. Hel, 10 (1938), 226-227.

M.E. Ozdemir, H. Kavurmaci, E. Set, Ostrowskifs type inequalities for (,m)-convex functions, Kyung-

pook Math. J. 50, 371.378, (2010).

M. Radulescu. S. Radulescu, P. Alexandrescu, On the Godunova-Levin-Schur class of functions,

Math. Inequal. Appl. 12(4), 853-862, (2009).

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-

M. Tunc, Ostrowski-type inequalities via h-convex functions with applications to speial means, J.

Ineq. Appl. 2013,2013:326.


  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)