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GENERALIZED WEIGHTED CEBYSEV AND OSTROWSKI TYPE INEQUALITIES FOR DOUBLE INTEGRALS

Yıl 2017, Cilt: 7 Sayı: 2, 272 - 281, 01.12.2017

Öz

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.

Kaynakça

  • 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.
Yıl 2017, Cilt: 7 Sayı: 2, 272 - 281, 01.12.2017

Öz

Kaynakça

  • 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.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

H. Budak Bu kişi benim

M. Z. Sarıkaya Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 7 Sayı: 2

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