Approximation by Genuine q-Bernstein-Durrmeyer Polynomials in Compact Disks  ABSTRACT  |  FULL TEXT 

Year 2011, Volume: 40 Issue: 1, 77 - 89, 01.01.2011

Nazim İdrisoglu Mahmudov

Keywords

-

References

• Anastassiou, G. A. and Gal, S. G. Approximation by complex Bernstein-Schurer and Kantorovich-Schurer polynomials in compact disks, Computers and Mathematics with Ap- plications 58 (4), 734–743, 2009.
• Anastassiou, G. A. and Gal, S. G. Approximation by complex Bernstein-Durrmeyer polyno- mials in compact disks, Mediterr. J. Math. DOI10.1007/s00009-010-0036-1, in press.
• Andrews, G E, Askey, R and Roy, R. Special Functions (Cambridge University Press, Cam- bridge, 1999).
• Chen, W. On the modified Bernstein-Durrmeyer operator, in: Report of the Fifth Chinese Conference on Approximation Theory, Zhen Zhou, China, 1987.
• Derriennic, M. -M. Modified Bernstein polynomials and Jacobi polynomials in q-calculus, Rendiconti Del Circolo Matematico Di Palermo, Serie II (Suppl.) 76, 269–290, 2005.
• DeVore, R. A. and Lorentz, G. G. Constructive Approximation (Springer, Berlin, 1993).
• Gal, S. G. Approximation by complex Bernstein-Stancu polynomials in compact disks, Re- sults in Mathematics 53 (3-4), 245–256, 2009.
• Gal, S. G. Exact orders in simultaneous approximation by complex Bernstein polynomials, J. Concr. Applic. Math. 7 (3), 215–220, 2009.
• Gal, S. G. Approximation by complex Bernstein and convolution type operators, Series on Concrete and Applicable Mathematics, 8 (World Scientific Publishing Co. Pte. Ltd., Hack- ensack, NJ, 2009) xii+337 pp.
• Gal, S. G. Shape Preserving Approximation by Real and Complex Polynomials (Birkhauser Publ., Boston, 2008).
• Gal, S. G. Approximation and geometric properties of complex Favard-Sz´asz-Mirakjan op- erators in compact disks, Computers and Mathematics with Applications 56, 1121–1127, 2008.
• Gal, S. G. Exact orders in simultaneous approximation by complex Bernstein-Stancu poly- nomials, Revue Anal. Num´eor. Approx. (Cluj) 37 (1), 47–52, 2008.
• Gal, S. G. Voronovskaja’s theorem and iterations for complex Bernstein polynomials in compact disks, Mediterr. J. Math. 5 (3), 253–272, 2008.
• Gal, S. G. Approximation by complex Bernstein-Kantorovich and Stancu- Kantorovich poly- nomials and their iterates in compact disks, Rev. Anal. Numer. Theor. Approx. (Cluj) 37 (2), 159–168, 2008.
• Gonska, H., Kacs´o, D. and Ra¸sa, I. On genuine Bernstein–Durrmeyer operators, Result. Math. 50, 213–225, 2007.
• Goodman, T. N. T. and Sharma, A. A Bernstein type operator on the simplex, Math. Balkan- ica 5, 129–145, 1991.
• Lorentz, G. G. Bernstein Polynomials (Chelsea, New York, 1986).
• Mahmudov, N. I. and Sabancıgil, P. On genuine q-Bernstein–Durrmeyer operators, Publ. Math. Debrecen, 76 (1-2), 2010, in press.
• Mahmudov, N. I. Convergence properties and iterations for q-Stancu polynomials in compact disks, Computer and Mathematics with Applications 59 (12), 3763–3769, 2010.
• Majid S. Foundations of quantum group theory (Cambridge University Press, Cambridge, 2000).
• Ostrovska, S. q-Bernstein polynomials and their iterates, J. Approx. Theory 123 (1), 232– 255, 2003.
• P´alt´anea, R. Approximation Theory using Positive Linear Operrators (Birkh¨auser, Boston, 2004).
• Parvanov, P. E. and Popov, B. D. The limit case of Bernstein’s operators with Jacobi weights, Math. Balkanica (N. S.) 8, 165–177, 1994.
• Phillips, G. M. A survey of results on the q-Bernstein polynomials, IMA J. Numer. Anal. 30(1), 277–288, 2010.
• Sauer, T. The genuine Bernstein–Durrmeyer operator on a simplex, Result. Math. 26, 99–130, 1994.
• Waldron, S. A generalised beta integral and the limit of the Bernstein–Durrmeyer operator with Jacobi weights, J. Approx. Theory 122, 141–150, 2003.