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SOME RL-INTEGRAL INEQUALITIES FOR THE WEIGHTED AND THE EXTENDED CHEBYSHEV FUNCTIONALS

Year 2017, Volume: 5 Issue: 1, 43 - 48, 01.04.2017

Abstract

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.

References

  • [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 de nis 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 di erential equations of fractional order. Springer Verlag, Wien, (1997), 223-276.
  • [10] D.S. Mitrinovic, Analytic inequalities. Springer Verlag. Berlin, (1970).
  • [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

Abstract

References

  • [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 de nis 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 di erential equations of fractional order. Springer Verlag, Wien, (1997), 223-276.
  • [10] D.S. Mitrinovic, Analytic inequalities. Springer Verlag. Berlin, (1970).
  • [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.
There are 14 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

ZOUBIR Dahmanı

AMINA Khamelı This is me

KARIMA Freha This is me

Publication Date April 1, 2017
Submission Date February 15, 2017
Acceptance Date July 24, 2016
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA 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.
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