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ON WEIGHTED MONTOGOMERY IDENTITIES FOR RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS

Year 2013, Volume: 1 Issue: 1, 48 - 53, 01.06.2013
https://izlik.org/JA94NY45RB

Abstract

In this paper, we extend the weighted Montogomery identitiesfor the Riemann-Liouville fractional integrals. We also use this Montogomeryidentities to establish some new Ostrowski type integral inequalities

References

  • G. Anastassiou, M.R. Hooshmandasl, A. Ghasemi and F. Moftakharzadeh, Montgomery iden- tities for fractional integrals and related fractional inequalities, J. Inequal. in Pure and Appl. Math, 10(4), 2009, Art. 97, 6 pp. [2] S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, J. Inequal. in Pure and Appl. Math, 10(3), 2009, Art. 97, 6 pp.
  • P. Cerone and S.S. Dragomir, Trapezoidal type rules from an inequalities point of view, Handbook of Analytic-Computational Methods in Applied Mathematics, CRC Press N.Y. (2000).
  • Z. Dahmani, L. Tabharit and S. Taf, Some fractional integral inequalities, Nonlinear Science Letters A, 2(1), 2010, p.155-160. [5] Z. Dahmani, L. Tabharit and S. Taf, New inequalities via Riemann-Liouville fractional inte- gration, J. Advance Research Sci. Comput., 2(1), 2010, p.40-45.
  • J. Duoandikoetxea, A unified approach to several inequalities involving functions and deriva- tives, Czechoslovak Mathematical Journal, 51 (126) (2001), 363–376.
  • R. Gorenflo, F. Mainardi, Fractionalcalculus: integral and differentiable equations of frac- tional order, Springer Verlag, Wien, 1997, p.223-276.
  • D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic Publishers, Dordrecht, 1991.
  • S.S. Dragomir and N. S. Barnett, An Ostrowski type inequality for mappings whose sec- ond derivatives are bounded and applications, RGMIA Research Report Collection, V.U.T., 1(1999), 67-76.
  • S.S. Dragomir, An Ostrowski type inequality for convex functions, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 16 (2005), 12–25.
  • Z. Liu, Some companions of an Ostrowski type inequality and application, J. Inequal. in Pure and Appl. Math, 10(2), 2009, Art. 52, 12 pp.
  • 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. Sarikaya, On the Ostrowski type integral inequality, Acta Math. Univ. Comenianae, Vol. LXXIX, 1(2010), pp. 129-134.
  • M. Z. Sarikaya, On the Ostrowski type integral inequality for double integrals, Demonstratio Mathematica, accepted.
  • M. Z. Sarikaya and H. Ogunmez, On the weighted Ostrowski type integral inequality for double integrals, The Arabian Journal for Science and Engineering (AJSE)-Mathematics, (2011) 36: 1153-1160
  • M.Z. Sarikaya and H. Ogunmez, On new inequalities via Riemann-Liouville fractional inte- gration, arXiv:1005.1167v1, submitted.
  • M.Z. Sarikaya, E. Set, H. Yaldiz and N., Basak, Hermite -Hadamard’s inequalities for frac- tional integrals and related fractional inequalities, Mathematical and Computer Modelling, DOI:10.1016/j.mcm.2011.12.048. [18] A. M. Ostrowski, ¨Uber die absolutabweichung einer differentiebaren funktion von ihrem in- tegralmitelwert, Comment. Math. Helv. 10(1938), 226-227.
  • Department of Mathematics, Faculty of Science and Arts, D¨uzce University, D¨uzce, Turkey
  • E-mail address: sarikayamz@gmail.com
  • E-mail address: yaldizhatice@gmail.com

Year 2013, Volume: 1 Issue: 1, 48 - 53, 01.06.2013
https://izlik.org/JA94NY45RB

Abstract

References

  • G. Anastassiou, M.R. Hooshmandasl, A. Ghasemi and F. Moftakharzadeh, Montgomery iden- tities for fractional integrals and related fractional inequalities, J. Inequal. in Pure and Appl. Math, 10(4), 2009, Art. 97, 6 pp. [2] S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, J. Inequal. in Pure and Appl. Math, 10(3), 2009, Art. 97, 6 pp.
  • P. Cerone and S.S. Dragomir, Trapezoidal type rules from an inequalities point of view, Handbook of Analytic-Computational Methods in Applied Mathematics, CRC Press N.Y. (2000).
  • Z. Dahmani, L. Tabharit and S. Taf, Some fractional integral inequalities, Nonlinear Science Letters A, 2(1), 2010, p.155-160. [5] Z. Dahmani, L. Tabharit and S. Taf, New inequalities via Riemann-Liouville fractional inte- gration, J. Advance Research Sci. Comput., 2(1), 2010, p.40-45.
  • J. Duoandikoetxea, A unified approach to several inequalities involving functions and deriva- tives, Czechoslovak Mathematical Journal, 51 (126) (2001), 363–376.
  • R. Gorenflo, F. Mainardi, Fractionalcalculus: integral and differentiable equations of frac- tional order, Springer Verlag, Wien, 1997, p.223-276.
  • D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic Publishers, Dordrecht, 1991.
  • S.S. Dragomir and N. S. Barnett, An Ostrowski type inequality for mappings whose sec- ond derivatives are bounded and applications, RGMIA Research Report Collection, V.U.T., 1(1999), 67-76.
  • S.S. Dragomir, An Ostrowski type inequality for convex functions, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 16 (2005), 12–25.
  • Z. Liu, Some companions of an Ostrowski type inequality and application, J. Inequal. in Pure and Appl. Math, 10(2), 2009, Art. 52, 12 pp.
  • 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. Sarikaya, On the Ostrowski type integral inequality, Acta Math. Univ. Comenianae, Vol. LXXIX, 1(2010), pp. 129-134.
  • M. Z. Sarikaya, On the Ostrowski type integral inequality for double integrals, Demonstratio Mathematica, accepted.
  • M. Z. Sarikaya and H. Ogunmez, On the weighted Ostrowski type integral inequality for double integrals, The Arabian Journal for Science and Engineering (AJSE)-Mathematics, (2011) 36: 1153-1160
  • M.Z. Sarikaya and H. Ogunmez, On new inequalities via Riemann-Liouville fractional inte- gration, arXiv:1005.1167v1, submitted.
  • M.Z. Sarikaya, E. Set, H. Yaldiz and N., Basak, Hermite -Hadamard’s inequalities for frac- tional integrals and related fractional inequalities, Mathematical and Computer Modelling, DOI:10.1016/j.mcm.2011.12.048. [18] A. M. Ostrowski, ¨Uber die absolutabweichung einer differentiebaren funktion von ihrem in- tegralmitelwert, Comment. Math. Helv. 10(1938), 226-227.
  • Department of Mathematics, Faculty of Science and Arts, D¨uzce University, D¨uzce, Turkey
  • E-mail address: sarikayamz@gmail.com
  • E-mail address: yaldizhatice@gmail.com
There are 18 citations in total.

Details

Authors

M. Zeki Sarıkaya This is me

HaticeYaldız This is me

Submission Date April 4, 2015
Publication Date June 1, 2013
IZ https://izlik.org/JA94NY45RB
Published in Issue Year 2013 Volume: 1 Issue: 1

Cite

Vancouver 1.M. Zeki Sarıkaya, HaticeYaldız . ON WEIGHTED MONTOGOMERY IDENTITIES FOR RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS. Konuralp J. Math. [Internet]. 2013 Apr. 1;1(1):48-53. Available from: https://izlik.org/JA94NY45RB
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