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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.

Abstract

Let , be the -Bernstein polynomials of a function . It has been known that, in general, the sequence with is not an approximating sequence for , in contrast to the standard case . In this paper, we give the sufficient and necessary condition under which the sequence approximates for any in the case . Based on this condition, we get that if for sufficiently large , then approximates for any . On the other hand, if can approximate for any in the case , then the sequence satisfies .