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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2014 / Cilt: 63 - Sayı: 2

APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS

Nurhayat ISPİR
Nesibe MANAV
Pages
23–39
Publication Date
2014-08-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also we give the exact order of approximation

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we study the approximation properties of the Stancutype bivariate generalization of the complex Baskakov operators.
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Key Findings & Data:We obtaina Voronovskaja type result with quantitative estimates for bivariate complexBaskakov-Stancu operators attached to analytic functions having suitable exponential growth on compact polydisks.
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Conclusion & Impact:Also we give the exact order of approximation
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bivariate complex Baskakov-Stancu operators · rate of convergence · exact order

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

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Cite This Article

ISPİR, N., MANAV, N. (2014). APPROXIMATION BY THE BIVARIATE COMPLEX BASKAKOV-STANCU OPERATORS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 63 - Sayı: 2, 23–39. https://ajindex.com/articles/747362

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References (12)

  1. 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).
  2. 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.
  3. 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).
  4. 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).
  5. Gal, S.G.: Approximation by complex Bernstein-Stancu polynomials in compact disks. Re- sults Math.53, 245-256 (2009).
  6. Gal, S.G.; Approximation by Complex Bernstein and Convoluation Type Operators. World Scienti…c, Sigapore (2009).
  7. Gal, S.G.: Exact orders in simultaneous approximation by complex Bernstein-Stancu poly- nomials. Rev. Anal. Numér.Théor. Approx.37, 47-52 (2008).
  8. Mahmudov, NI, Gupta, V: Approximation by genuine Durrmeyer-Stancu polynomials in com- pact disks. Math. Comput. Model.55, 278-285, (2012).
  9. 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).
  10. Pethe, S.: On the Baskakov operators. Indian J. Math.26(1–3), 43–48 (1984).
  11. 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).
  12. 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).