On Some Double Weighted Fractional Integral Inequalities
DOI:
https://doi.org/10.5644/SJM.15.01.03Keywords:
Riemann-Liouville fractional integral, double weighted Chebyshev functionalAbstract
In this paper, we establish new double weighted results of Chebyshev inequalities involving the Riemann-Liouville fractional integral operator with respect to another measurable, increasing, positive and monotone function. In particular, some recent results are deduced as some special cases.
Downloads
References
K. M.Awan, J. Pecaric, A. Rehman, Steffensen's generalization of Chebyshev inequality, J. Math. Inequal., 9 (1) (2015), 155-163.
M. Bezziou, Z. Dahmani and A. Khameli, Some Weighted Inequalities of Chebyshev Type Via RL-Approach, Mathematica., 60 (83) (2018), 12--20.
P.L. Chebyshev, Sur les expressions approximatives des integrales definis par les autres prises entre les memes limite, Proc. Math. Soc. Charkov, (1882), 93-98.
Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci. (IJNS)., 9 (4) (2010), 493-497.
Z. Dahmani, About some integral inequalities using Riemann-Liouville integrals, Gen. Math., 20 (4) (2012), 63-69.
Z. Dahmani, O. Mechouar, S. Brahami, Certain inequalities related to the Chebyshev's functional involving Riemann-Liouville operator, BMATHAA Bulletin, 3 (4) (2011), 38-44.
Z. Dahmani and M. Doubbi Bounoua, Further results on Chebyshev and Steffensen inequalities, Kyungpook. Math. J., 58 (2018), 55-66.
H.J. Godwin, On Generalizations of Chebyshev Inequality, J. Amer. Statist. Assoc., 5 (27) (1955), 923-945.
C.P. Niculescu, An extension of Chebyshev's inequality and its connection with Jensen's inequality, J. Inequal. Appl., 6 (3) (2001), 451-462.
A.M. Ostrowski, On an integral inequality, Aequationes Math., 4 (2) (1970), 358-373.
B.G. Pachpatte, A note on Chebyshev-Grüss type inequalities for differential functions, Tamsui Oxf. J. Math. Sci., 22 (1) (2006), 29-36.
S.G. Samko, A.A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives Theory and Application, Gordan and Breach Science, New York., 1993.
M.Z. Sarikatya, H. Yaldiz, New generalization fractional inequalities of Ostrowski-Gruss type, Lobachevskii J. Math., 34 (4) (2013), 326-331.
M.Z. Sarikatya, On the Ostrowski type integral inequality , Acta Math. Univ. Comenianaen., LXXIX (1) (2010), 129-134.
