Abstract and Applied Analysis
Volume 2011 (2011), Article ID 609431, 13 pages
doi:10.1155/2011/609431
Research Article

A de Casteljau Algorithm for 𝑞 -Bernstein-Stancu Polynomials

The Great Poland University of Social and Economics in Środa Wielkopolska, Paderewskiego 27, 63-000 Środa Wielkopolska, Poland

Received 17 September 2010; Accepted 7 January 2011

Academic Editor: Wolfgang Ruess

Copyright © 2011 Grzegorz Nowak. 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

This paper is concerned with a generalization of the 𝑞 -Bernstein polynomials and Stancu operators, where the function is evaluated at intervals which are in geometric progression. It is shown that these polynomials can be generated by a de Casteljau algorithm, which is a generalization of that relating to the classical case and 𝑞 -Bernstein case.