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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 185948, 19 pages
doi:10.1155/2012/185948
Research Article
On the Sets of Convergence for Sequences of the -Bernstein Polynomials with
Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey
Received 27 March 2012; Accepted 19 June 2012
Academic Editor: Ngai-Ching Wong
Copyright © 2012 Sofiya Ostrovska and Ahmet Yaşar Özban. 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
- G. E. Andrews, R. Askey, and R. Roy, Special Functions, vol. 71, Cambridge University Press, Cambridge, UK, 1999. View at Zentralblatt MATH
- S. Ostrovska, βThe first decade of the -Bernstein polynomials: results and perspectives,β Journal of Mathematical Analysis and Approximation Theory, vol. 2, no. 1, pp. 35β51, 2007.
- N. Mahmudov, βThe moments of -Bernstein operators in the case ,β Numerical Algorithms, vol. 53, no. 4, pp. 439β450, 2010. View at Publisher Β· View at Google Scholar
- M. Popov, βNarrow operators (a survey),β in Function Spaces IX, vol. 92, pp. 299β326, Banach Center Publications, 2011. View at Publisher Β· View at Google Scholar
- P. Sabancıgil, βHigher order generalization of -Bernstein operators,β Journal of Computational Analysis and Applications, vol. 12, no. 4, pp. 821β827, 2010.
- H. Wang, βProperties of convergence for -Bernstein polynomials,β Journal of Mathematical Analysis and Applications, vol. 340, no. 2, pp. 1096β1108, 2008. View at Publisher Β· View at Google Scholar
- Z. Wu, βThe saturation of convergence on the interval for the -Bernstein polynomials in the case ,β Journal of Mathematical Analysis and Applications, vol. 357, no. 1, pp. 137β141, 2009. View at Publisher Β· View at Google Scholar
- X.-M. Zeng, D. Lin, and L. Li, βA note on approximation properties of -Durrmeyer operators,β Applied Mathematics and Computation, vol. 216, no. 3, pp. 819β821, 2010. View at Publisher Β· View at Google Scholar
- C. A. Charalambides, βThe -Bernstein basis as a -binomial distribution,β Journal of Statistical Planning and Inference, vol. 140, no. 8, pp. 2184β2190, 2010. View at Publisher Β· View at Google Scholar
- S. C. Jing, βThe -deformed binomial distribution and its asymptotic behaviour,β Journal of Physics A, vol. 27, no. 2, pp. 493β499, 1994. View at Publisher Β· View at Google Scholar
- I. Ya. Novikov and S. B. Stechkin, βFundamentals of wavelet theory,β Russian Mathematical Surveys, vol. 53, no. 6, pp. 53β128, 1998. View at Publisher Β· View at Google Scholar
- M. I. Ostrovskiĭ, βRegularizability of inverse linear operators in Banach spaces with a basis,β Siberian Mathematical Journal, vol. 33, no. 3, pp. 470β476, 1992. View at Publisher Β· View at Google Scholar
- V. S. Videnskii, βOn some classes of -parametric positive linear operators,β in Selected Topics in Complex Analysis, vol. 158, pp. 213β222, Birkhäuser, Basel, Switzerland, 2005. View at Publisher Β· View at Google Scholar
- A. Il'inskii and S. Ostrovska, βConvergence of generalized Bernstein polynomials,β Journal of Approximation Theory, vol. 116, no. 1, pp. 100β112, 2002. View at Publisher Β· View at Google Scholar Β· View at Scopus
- S. Ostrovska, β-Bernstein polynomials and their iterates,β Journal of Approximation Theory, vol. 123, no. 2, pp. 232β255, 2003. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
- S. Ostrovska and A. Y. Özban, βThe norm estimates of the -Bernstein operators for varying ,β Computers & Mathematics with Applications, vol. 62, no. 12, pp. 4758β4771, 2011. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
- S. Ostrovska, βOn the approximation of analytic functions by the -Bernstein polynomials in the case ,β Electronic Transactions on Numerical Analysis, vol. 37, pp. 105β112, 2010.
- I. J. Schoenberg, βOn polynomial interpolation at the points of a geometric progression,β Proceedings of the Royal Society of Edinburgh, vol. 90, no. 3-4, pp. 195β207, 1981. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
- A. Pinkus, βWeierstrass and approximation theory,β Journal of Approximation Theory, vol. 107, no. 1, pp. 1β66, 2000. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
- G. G. Lorentz, Bernstein Polynomials, Chelsea, New York, NY, USA, 2nd edition, 1986.
- S. Cooper and S. Waldron, βThe eigenstructure of the Bernstein operator,β Journal of Approximation Theory, vol. 105, no. 1, pp. 133β165, 2000. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
- R. A. DeVore and G. G. Lorentz, Constructive Aapproximation, vol. 303, Springer, Berlin, Germany, 1993.