In this paper, we use the Riemann-Liouville fractional integrals to establish some new integral inequalities related to the weighted and the extended Chebyshev functionals. Some classical results are also presented.
[1] S. Belarbi, Z. Dahmani, On some new fractional integral inequalities. JIPAM Vol:10, No.3, (2009), 1-9.
[2] P.L. Chebyshev, Sur les expressions approximatives des integrales denis par les autres prises entre les memes limite. Proc. Math. Soc. Charkov, 2, (1882), 93-98.
[3] Z. Dahmani, New inequalities in fractional integrals. International Journal of Nonlinear Sciences, Vol:9, No.4 (2010), 493-497.
[4] Z. Dahmani, About some integral inequalities using Riemann-Liouville integrals. General Mathematics. Vol:20, No.4 (2012), 63-69.
[5] Z. Dahmani, O. Mechouar, S. Brahami, Certain inequalities related to the Chebyshev's functional involving Riemann-Liouville operator. Bulletin of Mathematical Analysis and Applications Vol:3, No.4 (2011), 38-44.
[6] Z. Dahmani, L. Tabharit, On weighted Gruss type inequalities via fractional integrals, JARPM, Journal of Advanced Research in Pure Mathematics, Vol:2, No.4 (2010), 31-38.
[7] S.S. Dragomir, A generalization of Gruss inequality in inner product spaces and applications. J. Math. Annal. Appl.,Vol:273, No.1 (1999), 74-82.
[8] N. Elezovic, L. Marangunic, G. Pecaric, Some improvements of Gruss type inequality. JMI Vol:1, No.3 (2007), 425-436.
[9] R. Goren o, F. Mainardi, Fractional calculus, integral and dierential equations of fractional order. Springer Verlag, Wien, (1997), 223-276.
[11] A. McD Mercer, An improvement of Gruss inequality. JIPAM, Vol:10, No.4 (2005), Art.93.
[12] A. McD Mercer, P. Mercer, New proofs of the Gruss inequality. Aust. J. Math. Anal. Appl.,Vol:1, No.2 (2004), Art.12.
[13] M.Z. Sarikaya, H. Yaldiz, New generalization fractional inequalities of Ostrowski-Gruss type. Lobachevskii Journal of Mathematics, Vol:34, No.4 (2013), 326{331.
[14] M.Z. Sarikaya, N. Aktan, H. Yildirim, On weighted Chebyshev-Gruss like inequalities on time scales. J. Math. Inequal., Vol:2, No.2 (2008), 185-195.
Year 2017,
Volume: 5 Issue: 1, 43 - 48, 01.04.2017
[1] S. Belarbi, Z. Dahmani, On some new fractional integral inequalities. JIPAM Vol:10, No.3, (2009), 1-9.
[2] P.L. Chebyshev, Sur les expressions approximatives des integrales denis par les autres prises entre les memes limite. Proc. Math. Soc. Charkov, 2, (1882), 93-98.
[3] Z. Dahmani, New inequalities in fractional integrals. International Journal of Nonlinear Sciences, Vol:9, No.4 (2010), 493-497.
[4] Z. Dahmani, About some integral inequalities using Riemann-Liouville integrals. General Mathematics. Vol:20, No.4 (2012), 63-69.
[5] Z. Dahmani, O. Mechouar, S. Brahami, Certain inequalities related to the Chebyshev's functional involving Riemann-Liouville operator. Bulletin of Mathematical Analysis and Applications Vol:3, No.4 (2011), 38-44.
[6] Z. Dahmani, L. Tabharit, On weighted Gruss type inequalities via fractional integrals, JARPM, Journal of Advanced Research in Pure Mathematics, Vol:2, No.4 (2010), 31-38.
[7] S.S. Dragomir, A generalization of Gruss inequality in inner product spaces and applications. J. Math. Annal. Appl.,Vol:273, No.1 (1999), 74-82.
[8] N. Elezovic, L. Marangunic, G. Pecaric, Some improvements of Gruss type inequality. JMI Vol:1, No.3 (2007), 425-436.
[9] R. Goren o, F. Mainardi, Fractional calculus, integral and dierential equations of fractional order. Springer Verlag, Wien, (1997), 223-276.
[11] A. McD Mercer, An improvement of Gruss inequality. JIPAM, Vol:10, No.4 (2005), Art.93.
[12] A. McD Mercer, P. Mercer, New proofs of the Gruss inequality. Aust. J. Math. Anal. Appl.,Vol:1, No.2 (2004), Art.12.
[13] M.Z. Sarikaya, H. Yaldiz, New generalization fractional inequalities of Ostrowski-Gruss type. Lobachevskii Journal of Mathematics, Vol:34, No.4 (2013), 326{331.
[14] M.Z. Sarikaya, N. Aktan, H. Yildirim, On weighted Chebyshev-Gruss like inequalities on time scales. J. Math. Inequal., Vol:2, No.2 (2008), 185-195.
Dahmanı, Z., Khamelı, A., & Freha, K. (2017). SOME RL-INTEGRAL INEQUALITIES FOR THE WEIGHTED AND THE EXTENDED CHEBYSHEV FUNCTIONALS. Konuralp Journal of Mathematics, 5(1), 43-48.
AMA
Dahmanı Z, Khamelı A, Freha K. SOME RL-INTEGRAL INEQUALITIES FOR THE WEIGHTED AND THE EXTENDED CHEBYSHEV FUNCTIONALS. Konuralp J. Math. April 2017;5(1):43-48.
Chicago
Dahmanı, ZOUBIR, AMINA Khamelı, and KARIMA Freha. “SOME RL-INTEGRAL INEQUALITIES FOR THE WEIGHTED AND THE EXTENDED CHEBYSHEV FUNCTIONALS”. Konuralp Journal of Mathematics 5, no. 1 (April 2017): 43-48.
EndNote
Dahmanı Z, Khamelı A, Freha K (April 1, 2017) SOME RL-INTEGRAL INEQUALITIES FOR THE WEIGHTED AND THE EXTENDED CHEBYSHEV FUNCTIONALS. Konuralp Journal of Mathematics 5 1 43–48.
IEEE
Z. Dahmanı, A. Khamelı, and K. Freha, “SOME RL-INTEGRAL INEQUALITIES FOR THE WEIGHTED AND THE EXTENDED CHEBYSHEV FUNCTIONALS”, Konuralp J. Math., vol. 5, no. 1, pp. 43–48, 2017.
ISNAD
Dahmanı, ZOUBIR et al. “SOME RL-INTEGRAL INEQUALITIES FOR THE WEIGHTED AND THE EXTENDED CHEBYSHEV FUNCTIONALS”. Konuralp Journal of Mathematics 5/1 (April 2017), 43-48.
JAMA
Dahmanı Z, Khamelı A, Freha K. SOME RL-INTEGRAL INEQUALITIES FOR THE WEIGHTED AND THE EXTENDED CHEBYSHEV FUNCTIONALS. Konuralp J. Math. 2017;5:43–48.
MLA
Dahmanı, ZOUBIR et al. “SOME RL-INTEGRAL INEQUALITIES FOR THE WEIGHTED AND THE EXTENDED CHEBYSHEV FUNCTIONALS”. Konuralp Journal of Mathematics, vol. 5, no. 1, 2017, pp. 43-48.
Vancouver
Dahmanı Z, Khamelı A, Freha K. SOME RL-INTEGRAL INEQUALITIES FOR THE WEIGHTED AND THE EXTENDED CHEBYSHEV FUNCTIONALS. Konuralp J. Math. 2017;5(1):43-8.