APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS

Nurhayat Ispir; Nesibe Manav

doi:10.1501/Commua1_0000000709

APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS

Year 2014, Volume: 63 Issue: 2, 23 - 39, 01.08.2014

Nurhayat Ispir Nesibe Manav

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

Keywords

Bivariate complex Baskakov-Stancu operators, rate of convergence, exact order

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

Nurhayat Ispir Nesibe Manav

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 This is me
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.