Fractional integral Chebyshev inequality without synchronous functions condition

Zoubir DAHMANI; Amina KHAMELI; Karima FREHA

doi:10.26637/mjm403/014

Abstract

In this paper, we use the Riemann-Liouville fractional integrals to establish some new integral inequalities related to the Chebyshev inequality in the case where the synchronicity of the given functions is replaced by another condition. This paper generalises some recent results in the paper of [C.P. Niculescu and I. Roventa: An extension of Chebyshev’s algebraic inequality, Math. Reports, 2013].

Keywords:

Integral inequalities, Riemann-Liouville integral, Chebyshev inequality

Mathematics Subject Classification:

26D10, 26A33

Authors Imprint References Funding Related Articles Downloads

Zoubir DAHMANI Laboratory LPAM, Faculty SEI, UMAB, Mostaganem, Algeria.
Amina KHAMELI Laboratory LPAM, Faculty SEI, UMAB, Mostaganem, Algeria.
Karima FREHA Laboratory LPAM, Faculty SEI, UMAB, Mostaganem, Algeria.

Pages: 448-452
Date Published: 01-07-2016
Vol. 4 No. 03 (2016): Malaya Journal of Matematik (MJM)

S. Belarbi, Z. Dahmani: On some new fractional integral inequalities. JIPAM Journal, 10(03), (2009), 1-9. DOI: https://doi.org/10.26637/mjm103/001

P.L. Chebyshev: Sur les expressions approximatives des integrales definies par les autres prises entre les memes limite. Proc. Math. Soc. Charkov, 2, (1882), 93-98.

Z. Dahmani: New inequalities in fractional integrals. International Journal of Nonlinear Sciences, 9(4), $(2010), 493-497$.

Z. Dahmani: About some integral inequalities using Riemann-Liouville integrals. General Mathematics. $20(4),(2012), 63-69$

Z. Dahmani, O. Mechouar, S. Brahami: Certain inequalities related to the Chebyshev's functional involving Riemann-Liouville operator. Bulletin of Mathematical Analysis and Applications 3 (4), (2011), 38-44.

Z. Dahmani, L. Tabharit: On weighted Gruss type inequalities via fractional integrals. JARPM, Journal of Advanced Research in Pure Mathematics, 2(4), (2010), 31-38. DOI: https://doi.org/10.5373/jarpm.392.032110

N. Elezovic, L. Marangunic, G. Pecaric: Some improvements of Gruss Type inequality. J. Math. Inequal. $1(3),(2007), 425-436$. DOI: https://doi.org/10.7153/jmi-01-36

R. Gorenflo, F. Mainardi: Fractional calculus: integral and differential equations of fractional order. Springer Verlag, Wien, (1997), 223-276 DOI: https://doi.org/10.1007/978-3-7091-2664-6_5

S.M. Malamud: Some complements to the Jenson and Chebyshev inequalities and a problem of W. Walter, Proc. Amer. Math. Soc., 129(9), (2001), 2671-2678. DOI: https://doi.org/10.1090/S0002-9939-01-05849-X

D.S. Mitrinovic: Analytic inequalities. Springer Verlag. Berlin, (1970). DOI: https://doi.org/10.1007/978-3-642-99970-3

C.P. Niculescu, I. Roventa: An extention of Chebyshev's algebric inequality. Math. Reports 15 (65), (2013), $91-95$

B.G. Pachpatte: A note on Chebyshev-Grüss type inequalities for differential functions. Tamsui Oxford Journal of Mathematical Sciences, 22(1), (2006), 29-36.

M.Z. Sarikaya, N. Aktan, H. Yildirim: On weighted Chebyshev-Gruss like inequalities on time scales, J. Math. Inequal., 2(2), (2008), 185-195. DOI: https://doi.org/10.7153/jmi-02-17

M.Z. Sarikaya, A. Saglam, and H. Yildirim: On generalization of Chebysev type inequalities, Iranian J. of Math. Sci. and Inform., 5(1), (2010), 41-48.

M.Z. Sarikaya, M.E. Kiris: On Ostrowski type inequalities and Chebyshev type inequalities with applications. Filomat, 29(8), (2015), 123-130. DOI: https://doi.org/10.2298/FIL1508695K

E. Set, M.Z. Sarikaya, F. Ahmad: A generalization of Chebyshev type inequalities for first defferentiable mappings. Miskolc Mathematical Notes, 12(2), (2011), 245-253. DOI: https://doi.org/10.18514/MMN.2011.338