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GENERALIZED WEIGHTED CEBYSEV AND OSTROWSKI TYPE INEQUALITIES FOR DOUBLE INTEGRALS

Year 2017, Volume: 7 Issue: 2, 272 - 281, 01.12.2017

Abstract

In this paper, we rstly establish generalized weighted Montgomery identity for double integrals. Then, some generalized weighted Cebysev and Ostrowski type inequalities for double integrals are given.

References

  • Ahmad,F., Barnett,N.S., and Dragomir,S.S., (2009), New weighted Ostrowski and ˇCebysev type in- equalities, Nonlinear Anal., 71(12), pp.1408-1412.
  • Barnett,N.S. and Dragomir,S.S., (2001), An Ostrowski type inequality for double integrals and appli- cations for cubature formulae, Soochow J. Math., 27(1), pp.109-114.
  • Boukerrioua,K. and Guezane-Lakoud,A., (2007), On generalization of ˇCebysev type inequalities, J.
  • Inequal. Pure and Appl. Math., 8(2), Art 55. ˇCebysev,P.L., (1882), Sur les expressions approximatives des integrales definies par les autres prises entre les mˇ
  • Cerone,P. and Dragomir,S.S., (2004), Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions, Demonstratio Math., 37(2), pp.299-308.
  • Dragomir,S.S., Cerone,P., Barnett,N.S., and Roumeliotis,J., (2000), An inequality of the Ostrowski type for double integrals and applications for cubature formulae, Tamsui Oxf. J. Math. Sci. 16(1), pp.1-16.
  • Guazene-Lakoud,A. and Aissaoui,F., (2011), New ˇCebysev type inequalities for double integrals, J. Math. Inequal, 5(4), pp.453-462.
  • Guazene-Lakoud,A. and Aissaoui,F., (2012), New double integrals weighted ˇCebyˇsev type inequalities
  • Journal of Mathematics and System Science 2, pp.286-291. Mitrinovic,D.S., Peˇcariˇc,J.E., and Fink,A. M., (1993), Classical and new inequalities in analysis, ser.
  • Math. Appl. (East European Ser.). Dordrecht: Kluwer Academic Publishers Group, Vol.61. Ostrowski,A.M., (1938), ¨Uber die absolutabweichung einer differentiebaren funktion von ihrem inte- gralmitelwert, Comment. Math. Helv. 10, pp.226-227.
  • Pachpatte,B.G., (2007), New inequalities of ˇCebysev type for double integrals, Demonstratio Mathe- matica, XI(1), pp.43-50.
  • Pachpatte,B.G., (2006), On ˇCebysev-Gr¨uss type inequalities via Pecaric’s extention of the Montgomery identity,J. Inequal. Pure and Appl. Math. 7(1), Art 11.
  • Rafiq,A., Shahbaz,Q., and Acu,A.M., (2009), The generalized ˇCebysev type inequality, ”Vasile Alec- sandri” University of Bacau Faculty of Sciences Scientic Studies and Research Series Mathematics and Informatics 19(1), pp.195-200.
  • Sarikaya,M.Z., Set,E., Ozdemir,M.E., and Dragomir,S.S., (2012), New some Hadamard’s type inequal- ities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2), pp.137-152.
  • Sarikaya,M.Z., Budak,H., and Yaldiz,H., (2014), ˇCebysev type inequalities for co-ordinated convex functions, Pure and Applied Mathematics Letters 2, pp.44-48.
  • Sarikaya,M.Z., Aktan,N., and Yıldırım,H., (2008), On weighted ˇCebysev-Gr¨uss type inequalities on time scales, J. Math. Inequal. 2(2), pp.185–195.
  • Sarikaya,M.Z., (2015), On the generalized weighted integral inequality for double integrals, Annals of the Alexandru Ioan Cuza University-Mathematics, LXI, pp.169-179. DOI: 10.2478/aicu-2014-0008.
  • Sarikaya,M.Z., (2012)On the Ostrowski type integral inequality for double integrals, Demonstratio Mathematica, XLV(3), pp.533-540.
  • Sarikaya,M.Z., Yaldiz,H., and Erden,S., (2014), On the weigted Ostrowski type inequalities for double integrals, Kragujevac Journal of Mathematics, 38(2), pp.303-314.
  • Set,E., Sarikaya,M.Z., and Ahmad,F., (2011), A generalization of Chebychev type inequalities for first differentiable mappings, Miskolc Mathematical Notes, 12(2), pp.245-253.
  • Set,E., Sarikaya,M.Z., and Ahmad,F., (2015), On weighted Ostrowski type inequalities for double in- tegrals, Pure and Applied Mathematics Letters, Volume 2015, pp.55-58.
Year 2017, Volume: 7 Issue: 2, 272 - 281, 01.12.2017

Abstract

References

  • Ahmad,F., Barnett,N.S., and Dragomir,S.S., (2009), New weighted Ostrowski and ˇCebysev type in- equalities, Nonlinear Anal., 71(12), pp.1408-1412.
  • Barnett,N.S. and Dragomir,S.S., (2001), An Ostrowski type inequality for double integrals and appli- cations for cubature formulae, Soochow J. Math., 27(1), pp.109-114.
  • Boukerrioua,K. and Guezane-Lakoud,A., (2007), On generalization of ˇCebysev type inequalities, J.
  • Inequal. Pure and Appl. Math., 8(2), Art 55. ˇCebysev,P.L., (1882), Sur les expressions approximatives des integrales definies par les autres prises entre les mˇ
  • Cerone,P. and Dragomir,S.S., (2004), Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions, Demonstratio Math., 37(2), pp.299-308.
  • Dragomir,S.S., Cerone,P., Barnett,N.S., and Roumeliotis,J., (2000), An inequality of the Ostrowski type for double integrals and applications for cubature formulae, Tamsui Oxf. J. Math. Sci. 16(1), pp.1-16.
  • Guazene-Lakoud,A. and Aissaoui,F., (2011), New ˇCebysev type inequalities for double integrals, J. Math. Inequal, 5(4), pp.453-462.
  • Guazene-Lakoud,A. and Aissaoui,F., (2012), New double integrals weighted ˇCebyˇsev type inequalities
  • Journal of Mathematics and System Science 2, pp.286-291. Mitrinovic,D.S., Peˇcariˇc,J.E., and Fink,A. M., (1993), Classical and new inequalities in analysis, ser.
  • Math. Appl. (East European Ser.). Dordrecht: Kluwer Academic Publishers Group, Vol.61. Ostrowski,A.M., (1938), ¨Uber die absolutabweichung einer differentiebaren funktion von ihrem inte- gralmitelwert, Comment. Math. Helv. 10, pp.226-227.
  • Pachpatte,B.G., (2007), New inequalities of ˇCebysev type for double integrals, Demonstratio Mathe- matica, XI(1), pp.43-50.
  • Pachpatte,B.G., (2006), On ˇCebysev-Gr¨uss type inequalities via Pecaric’s extention of the Montgomery identity,J. Inequal. Pure and Appl. Math. 7(1), Art 11.
  • Rafiq,A., Shahbaz,Q., and Acu,A.M., (2009), The generalized ˇCebysev type inequality, ”Vasile Alec- sandri” University of Bacau Faculty of Sciences Scientic Studies and Research Series Mathematics and Informatics 19(1), pp.195-200.
  • Sarikaya,M.Z., Set,E., Ozdemir,M.E., and Dragomir,S.S., (2012), New some Hadamard’s type inequal- ities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2), pp.137-152.
  • Sarikaya,M.Z., Budak,H., and Yaldiz,H., (2014), ˇCebysev type inequalities for co-ordinated convex functions, Pure and Applied Mathematics Letters 2, pp.44-48.
  • Sarikaya,M.Z., Aktan,N., and Yıldırım,H., (2008), On weighted ˇCebysev-Gr¨uss type inequalities on time scales, J. Math. Inequal. 2(2), pp.185–195.
  • Sarikaya,M.Z., (2015), On the generalized weighted integral inequality for double integrals, Annals of the Alexandru Ioan Cuza University-Mathematics, LXI, pp.169-179. DOI: 10.2478/aicu-2014-0008.
  • Sarikaya,M.Z., (2012)On the Ostrowski type integral inequality for double integrals, Demonstratio Mathematica, XLV(3), pp.533-540.
  • Sarikaya,M.Z., Yaldiz,H., and Erden,S., (2014), On the weigted Ostrowski type inequalities for double integrals, Kragujevac Journal of Mathematics, 38(2), pp.303-314.
  • Set,E., Sarikaya,M.Z., and Ahmad,F., (2011), A generalization of Chebychev type inequalities for first differentiable mappings, Miskolc Mathematical Notes, 12(2), pp.245-253.
  • Set,E., Sarikaya,M.Z., and Ahmad,F., (2015), On weighted Ostrowski type inequalities for double in- tegrals, Pure and Applied Mathematics Letters, Volume 2015, pp.55-58.
There are 21 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

H. Budak This is me

M. Z. Sarıkaya This is me

Publication Date December 1, 2017
Published in Issue Year 2017 Volume: 7 Issue: 2

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