Abstract and Applied Analysis
Volume 2011 (2011), Article ID 294715, 10 pages
http://dx.doi.org/10.1155/2011/294715
Research Article

Some Identities on Bernstein Polynomials Associated with 𝑞 -Euler Polynomials

A. Bayad,1 T. Kim,2 B. Lee,3 and S.-H. Rim4

1Département de Mathématiques, Université d'Evry Val d'Essonne, Bboulevard F. Mitterrand, 91025 Evry Cedex, France
2Division of General Education-Mathematics, Kwang-Woon University, Seoul 139-701, Republic of Korea
3Department of Wireless Communications Engineering, Kwangwoon University, Seoul 139-701, Republic of Korea
4Department of Mathematics Education, Kyungpook National University, Taegu 702-701, Republic of Korea

Received 11 January 2011; Accepted 11 February 2011

Academic Editor: John Rassias

Copyright © 2011 A. Bayad 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.

Abstract

We investigate some interesting properties of the 𝑞 -Euler polynomials. The purpose of this paper is to give some relationships between Bernstein and 𝑞 -Euler polynomials, which are derived by the 𝑝 -adic integral representation of the Bernstein polynomials associated with 𝑞 -Euler polynomials.