Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 126319, 7 pages
http://dx.doi.org/10.1155/2014/126319
Research Article

The Truncated -Bernstein Polynomials in the Case

Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey

Received 23 December 2013; Accepted 21 January 2014; Published 5 March 2014

Academic Editor: Sofiya Ostrovska

Copyright © 2014 Mehmet Turan. 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. E. Andrews, R. Askey, and R. Roy, Special Functions, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, UK, 1999. View at MathSciNet
  2. G. M. Phillips, “Bernstein polynomials based on the q-integers,” Annals of Numerical Mathematics, vol. 4, no. 1–4, pp. 511–518, 1997. View at Google Scholar · View at MathSciNet
  3. 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
  4. S. Ostrovska, “The first decade of the q-Bernstein polynomials: results and perspectives,” Journal of Mathematical Analysis and Approximation Theory, vol. 2, no. 1, pp. 35–51, 2007. View at Google Scholar · View at MathSciNet
  5. O. Agratini, “On certain q-analogues of the Bernstein operators,” Carpathian Journal of Mathematics, vol. 24, no. 3, pp. 281–286, 2008. View at Google Scholar · View at Scopus
  6. G. Nowak, “Approximation properties for generalized q-Bernstein polynomials,” Journal of Mathematical Analysis and Applications, vol. 350, no. 1, pp. 50–55, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  7. S. Ostrovska and A. Y. Özban, “On the sets of convergence for sequences of the q-Bernstein polynomials with q>1,” Abstract and Applied Analysis, vol. 2012, Article ID 185948, 19 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  8. V. S. Videnskii, “On some classes of q-parametric positive linear operators,” in Operator Theory, Advances and Applications, vol. 158, pp. 213–222, 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. 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 · View at MathSciNet
  11. M. M. Popov, “An exact Daugavet type inequality for small into isomorphisms in L1,” Archiv der Mathematik, vol. 90, no. 6, pp. 537–544, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Cooper and S. Waldron, “The eigenstructure of the Bernstein operator,” Journal of Approximation Theory, vol. 105, no. 1, pp. 133–165, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. K. Kaşkaloğlu and S. Ostrovska, “On the q-Bernstein polynomials of piecewise linear functions in the case q>1,” Mathematical and Computer Modelling, vol. 57, no. 9-10, pp. 2419–2431, 2013. View at Publisher · View at Google Scholar