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APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS

Year 2014, Volume: 63 Issue: 2, 23 - 39, 01.08.2014
https://doi.org/10.1501/Commua1_0000000709

Abstract

In this paper we study the approximation properties of the Stancutype bivariate generalization of the complex Baskakov operators. We obtaina Voronovskaja type result with quantitative estimates for bivariate complexBaskakov-Stancu operators attached to analytic functions having suitable exponential growth on compact polydisks. Also we give the exact order of approximation

References

  • Atakut, Ç.: On the approximation of functions together with derivatives by certain linear positive operators. Commun. Fac. Sci. Univ. Ank. Ser. Phys.-Tech. Stat. 46(1-2), 57-65, (1997).
  • Barbosu, D.; Some generalized bivariate Berstein operators. Mathematical Notes (Miskolc) Vol. 1.(1), (2000), 3-10.
  • Barbosu,D., Bivariate Operators of Schurer-Stancu Type, An. St. Univ. Ovidius Constanta, Vol. 11 (1), (2003), 1–8.
  • Baskakov, V.A.; An example of a sequence of linear positive operators in the space of con- tinuous functions. Dokl. Akad. Nauk SSSR 113, 249-251, (1957) (in Russian).
  • Cao, F., Ding, C., Xu, Z.: On multivariate Baskakov operators. J. Math. Anal. Appl.307, –291, (2005).
  • Gal, S.G., Gupta, V., Verma, D.K., Agrawal, P.N.; Approximation by complex Baskakov- Stancu operators in compact disks. Rend. Circ. Math. Palermo 61, 153-165, (2012).
  • Gal, S.G.: Approximation by complex Bernstein-Stancu polynomials in compact disks. Re- sults Math.53, 245-256 (2009).
  • Gal, S.G.; Approximation by Complex Bernstein and Convoluation Type Operators. World Scienti…c, Sigapore (2009).
  • Gal, S.G.: Exact orders in simultaneous approximation by complex Bernstein-Stancu poly- nomials. Rev. Anal. Numér.Théor. Approx.37, 47-52 (2008).
  • Mahmudov, NI, Gupta, V: Approximation by genuine Durrmeyer-Stancu polynomials in com- pact disks. Math. Comput. Model.55, 278-285, (2012).
  • Mishra, V. N. , Khatri,K. and Mishra,L. N., On Simultaneous Approximation for BaskakovDurrmeyer-Stancu type operators, Journal of Ultra Scientist of Physical Sciences (3)A, 567-577,(2012).
  • Pethe, S.: On the Baskakov operators. Indian J. Math.26(1–3), 43–48 (1984).
  • Ren, Mei-Ying, Zeng Xiao-Ming and Zeng, L., Approximation by complex Durrmeyer-Stancu type operators in compact disks, J. Inequal. Appl. 2013, 2013:442.
  • Verma, D. K., Gupta, V., and Agrawal, P. N., Some approximationproperties of Baskakov Durrmeyer-Stancu operators, Appl. Math. Comp. 218,(11), 6549-6556, (2012).
  • Volkov, V. I., On the convergence of sequences of linear positive operators in the space of continuous functions of two variable, Matematicheskii Sbornik, vol. 43, no. 85, p. 504, 1957 (in Russian).
Year 2014, Volume: 63 Issue: 2, 23 - 39, 01.08.2014
https://doi.org/10.1501/Commua1_0000000709

Abstract

References

  • Atakut, Ç.: On the approximation of functions together with derivatives by certain linear positive operators. Commun. Fac. Sci. Univ. Ank. Ser. Phys.-Tech. Stat. 46(1-2), 57-65, (1997).
  • Barbosu, D.; Some generalized bivariate Berstein operators. Mathematical Notes (Miskolc) Vol. 1.(1), (2000), 3-10.
  • Barbosu,D., Bivariate Operators of Schurer-Stancu Type, An. St. Univ. Ovidius Constanta, Vol. 11 (1), (2003), 1–8.
  • Baskakov, V.A.; An example of a sequence of linear positive operators in the space of con- tinuous functions. Dokl. Akad. Nauk SSSR 113, 249-251, (1957) (in Russian).
  • Cao, F., Ding, C., Xu, Z.: On multivariate Baskakov operators. J. Math. Anal. Appl.307, –291, (2005).
  • Gal, S.G., Gupta, V., Verma, D.K., Agrawal, P.N.; Approximation by complex Baskakov- Stancu operators in compact disks. Rend. Circ. Math. Palermo 61, 153-165, (2012).
  • Gal, S.G.: Approximation by complex Bernstein-Stancu polynomials in compact disks. Re- sults Math.53, 245-256 (2009).
  • Gal, S.G.; Approximation by Complex Bernstein and Convoluation Type Operators. World Scienti…c, Sigapore (2009).
  • Gal, S.G.: Exact orders in simultaneous approximation by complex Bernstein-Stancu poly- nomials. Rev. Anal. Numér.Théor. Approx.37, 47-52 (2008).
  • Mahmudov, NI, Gupta, V: Approximation by genuine Durrmeyer-Stancu polynomials in com- pact disks. Math. Comput. Model.55, 278-285, (2012).
  • Mishra, V. N. , Khatri,K. and Mishra,L. N., On Simultaneous Approximation for BaskakovDurrmeyer-Stancu type operators, Journal of Ultra Scientist of Physical Sciences (3)A, 567-577,(2012).
  • Pethe, S.: On the Baskakov operators. Indian J. Math.26(1–3), 43–48 (1984).
  • Ren, Mei-Ying, Zeng Xiao-Ming and Zeng, L., Approximation by complex Durrmeyer-Stancu type operators in compact disks, J. Inequal. Appl. 2013, 2013:442.
  • Verma, D. K., Gupta, V., and Agrawal, P. N., Some approximationproperties of Baskakov Durrmeyer-Stancu operators, Appl. Math. Comp. 218,(11), 6549-6556, (2012).
  • Volkov, V. I., On the convergence of sequences of linear positive operators in the space of continuous functions of two variable, Matematicheskii Sbornik, vol. 43, no. 85, p. 504, 1957 (in Russian).
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Nurhayat Ispir This is me

Nesibe Manav

Publication Date August 1, 2014
Published in Issue Year 2014 Volume: 63 Issue: 2

Cite

APA Ispir, N., & Manav, N. (2014). APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 63(2), 23-39. https://doi.org/10.1501/Commua1_0000000709
AMA Ispir N, Manav N. APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2014;63(2):23-39. doi:10.1501/Commua1_0000000709
Chicago Ispir, Nurhayat, and Nesibe Manav. “APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63, no. 2 (August 2014): 23-39. https://doi.org/10.1501/Commua1_0000000709.
EndNote Ispir N, Manav N (August 1, 2014) APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63 2 23–39.
IEEE N. Ispir and N. Manav, “APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 63, no. 2, pp. 23–39, 2014, doi: 10.1501/Commua1_0000000709.
ISNAD Ispir, Nurhayat - Manav, Nesibe. “APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63/2 (August 2014), 23-39. https://doi.org/10.1501/Commua1_0000000709.
JAMA Ispir N, Manav N. APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63:23–39.
MLA Ispir, Nurhayat and Nesibe Manav. “APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 63, no. 2, 2014, pp. 23-39, doi:10.1501/Commua1_0000000709.
Vancouver Ispir N, Manav N. APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63(2):23-39.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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