Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON THE DEGREE OF APPROXIMATION FOR BIVARIATE LUPAS TYPE OPERATORS

  • Deo, Naokant (Department of Applied Mathematics, Delhi College of Engineering)
  • Received : 2009.11.17
  • Accepted : 2009.12.20
  • Published : 2010.09.30
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Abstract

The aim of this paper is to give some simultaneous approximation properties as well as differential properties, Voronovskaya type theorem, several asymptotic formulae for the partial derivative and the degree of approximation for two dimensional Lupas type operators.

Keywords

References

  1. V. A. Baskakov, An example of a sequence of linear positive operators in the space of continuous functions, DAN, 113(1957), 249-251 (in Russian).
  2. M. Becker, Global approximation theorems for Szaasz-Mirakyan and Baskakov operators in polynomial weight spaces, Indiana Univ. Math. J., 27(1) (1978), 127-142. https://doi.org/10.1512/iumj.1978.27.27011
  3. F. Cao and C. Ding and Z. Xu, On multivariate Baskakov operators, J. Math. Anal. Appl. 307 (2005), 274-291. https://doi.org/10.1016/j.jmaa.2004.10.061
  4. N. Deo, Direct result on the Durrmeyer variant of Beta operators, Southeast Asian Bull. Math., 32(2008), 283-290.
  5. F. Guo, On convergence rate of approximation for two-dimensional Baskakov operators, Anal. Theory Appl. 19 (2003), 273-279. https://doi.org/10.1007/BF02835286
  6. V. Gupta and A. Ahmad, Simultaneous approximation by modified Lupas, operators, Instanbul Uni. Fen. Fak. Mat. Der., 54(1995), 11-22.
  7. M. Gurdek, L. Rempulska and M. Skorupka, The Baskakov operators for functions of two variables, Collect. Math., 50(3) (1999), 289-302.
  8. V. Gupta and N. Deo, On the rate of convergence for bivariate Lupas, operators, General Math. 13(3) (2005), 107-114.
  9. G. G. Lorentz, Bernstein Polynomials, University of Toronto Press, Toronto, 1953.
  10. L. Rempulska and M. Skorupka, On strong approximation of functions of one and two variables by certain operator, Fasc. Math., 35(2005), 115-133.
  11. L. Rempulska and M. Skorupka, Approximation of differentiable functions of two variables by Baskakov operators, 5-th International Conference APLIMAT, (2006), 315-319.
  12. Q. Shen and J. Xu, Simultaneous approximation by multivariate Szaasz-Durrmeyer operator, J. of Hubei Uni. (NSE)(in Chinese), 21(2)(1999), 107-111.