Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2010, Article ID 706483, 12 pages
http://dx.doi.org/10.1155/2010/706483
Review Article

A Note on the Modified -Bernstein Polynomials

1Division of General Education, Kwangwoon University, Seoul 139-701, Republic of Korea
2Department of Mathematics and Computer Science, Konkuk University, Chungju 138-701, Republic of Korea
3Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea

Received 20 May 2010; Revised 11 July 2010; Accepted 14 July 2010

Academic Editor: Leonid Shaikhet

Copyright © 2010 Taekyun Kim et al. 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. S. Bernstein, “Demonstration du theoreme de Weierstrass, fondee sur le calcul des probabilities,” Communications of the Kharkov Mathematical Society, vol. 2, no. 13, pp. 1–2, 1912-1913. View at Google Scholar
  2. M. Acikgoz and S. Araci, “A study on the integral of the product of several type Bernstein polynomials,” IST Transaction of Applied Mathematics-Modelling and Simulation. In press.
  3. N. K. Govil and V. Gupta, “Convergence of q-Meyer-König-Zeller-Durrmeyer operators,” Advanced Studies in Contemporary Mathematics, vol. 19, no. 1, pp. 181–189, 2009. View at Google Scholar
  4. M. Acikgoz and S. Araci, “On the generating function of the Bernstein polynomials,” in Proceedings of the 8th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM '10), AIP, Rhodes, Greece, March 2010.
  5. Y. Simsek and M. Acikgoz, “A new generating function of q-Bernstein-type polynomials and their interpolation function,” Abstract and Applied Analysis, vol. 2010, Article ID 769095, 12 pages, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. 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 Zentralblatt MATH · View at MathSciNet
  7. T. Kim, “q-Volkenborn integration,” Russian Journal of Mathematical Physics, vol. 9, no. 3, pp. 288–299, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. T. Kim, “New approach to q-Euler polynomials of higher order,” Russian Journal of Mathematical Physics, vol. 17, no. 2, pp. 218–225, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. T. Kim, “Barnes-type multiple q-zeta functions and q-Euler polynomials,” Journal of Physics A: Mathematical and Theoretical, vol. 43, no. 25, Article ID 255201, 11 pages, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. T. Kim, “Note on the Euler q-zeta functions,” Journal of Number Theory, vol. 129, no. 7, pp. 1798–1804, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  11. T. Kim, S. D. Kim, and D.-W. Park, “On uniform differentiability and q-Mahler expansions,” Advanced Studies in Contemporary Mathematics, vol. 4, no. 1, pp. 35–41, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Zorlu, H. Aktuglu, and M. A. Özarslan, “An estimation to the solution of an initial value problem via q-Bernstein polynomials,” Journal of Computational Analysis and Applications, vol. 12, no. 3, pp. 637–645, 2010. View at Google Scholar · View at MathSciNet
  13. V. Gupta and C. Cristina, “Statistical approximation properties of q-Baskakov-Kantorovich operators,” Central European Journal of Mathematics. In press. View at Zentralblatt MATH