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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 259491, 6 pages
http://dx.doi.org/10.1155/2014/259491
Research Article

Approximation by -Bernstein Polynomials in the Case

Library, Capital Normal University, Beijing 100048, China

Received 24 December 2013; Accepted 8 February 2014; Published 12 March 2014

Academic Editor: Sofiya Ostrovska

Copyright © 2014 Xuezhi Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. M. Phillips, “Bernstein polynomials based on the q-integers,” Annals of Numerical Mathematics, vol. 4, pp. 511–518, 1997. View at MathSciNet
  2. H. Wang and S. Ostrovska, “The norm estimates for the q-Bernstein operator in the case q>1,” Mathematics of Computation, vol. 79, no. 269, pp. 353–363, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  3. G. M. Phillips, “A generalization of the Bernstein polynomials based on the q-integers,” The Australian & New Zealand Industrial and Applied Mathematics Journal, vol. 42, no. 1, pp. 79–86, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  4. G. M. Phillips, “A survey of results on the q-Bernstein polynomials,” IMA Journal of Numerical Analysis, vol. 30, no. 1, pp. 277–288, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  5. A. Il'inskii, “A probabilistic approach to q-polynomial coefficients, Euler and Stirling numbers. I,” Matematicheskaya Fizika, Analiz, Geometriya, vol. 11, no. 4, pp. 434–448, 2004. View at MathSciNet
  6. Z. Finta, “Direct and converse results for q-Bernstein operators,” Proceedings of the Edinburgh Mathematical Society, vol. 52, no. 2, pp. 339–349, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  7. A. Il'inskii and S. Ostrovska, “Convergence of generalized Bernstein polynomials,” Journal of Approximation Theory, vol. 116, no. 1, pp. 100–112, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  8. V. S. Videnskii, “On some classes of q-parametric positive linear operators,” in Selected Topics in Complex Analysis, vol. 158 of Operator Theory: Advances and Applications, pp. 213–222, Birkhäuser, Basel, Switzerland, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  9. H. Wang, “Korovkin-type theorem and application,” Journal of Approximation Theory, vol. 132, no. 2, pp. 258–264, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Wang, “Voronovskaya-type formulas and saturation of convergence for q-Bernstein polynomials for 0<q<1,” Journal of Approximation Theory, vol. 145, no. 2, pp. 182–195, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  11. H. Wang and F. Meng, “The rate of convergence of q-Bernstein polynomials for 0<q<1,” Journal of Approximation Theory, vol. 136, no. 2, pp. 151–158, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  12. S. Ostrovska, “q-Bernstein polynomials and their iterates,” Journal of Approximation Theory, vol. 123, no. 2, pp. 232–255, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. S. Ostrovska, “The approximation by q-Bernstein polynomials in the case q1,” Archiv der Mathematik, vol. 86, no. 3, pp. 282–288, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  14. S. Ostrovska, “The approximation of all continuous functions on [0; 1] by q-Bernstein polynomials in the case q 1+,” Results in Mathematics, vol. 52, no. 1-2, pp. 179–186, 2008. View at Publisher · View at Google Scholar
  15. S. Ostrovska and A. Y. Özban, “The norm estimates of the q-Bernstein operators for varying q >1,” Computers & Mathematics with Applications, vol. 62, no. 12, pp. 4758–4771, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  16. H. Wang and X. Wu, “Saturation of convergence for q-Bernstein polynomials in the case q1,” Journal of Mathematical Analysis and Applications, vol. 337, no. 1, pp. 744–750, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Z. Wu, “The saturation of convergence on the interval [0; 1] for the q-Bernstein polynomials in the case q >1,” Journal of Mathematical Analysis and Applications, vol. 357, no. 1, pp. 137–141, 2009. View at Publisher · View at Google Scholar