Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 513821, 8 pages
doi:10.1155/2011/513821
Research Article

A Study on the 𝑝 -Adic 𝑞 -Integral Representation on ℤ 𝑝 Associated with the Weighted 𝑞 -Bernstein and 𝑞 -Bernoulli Polynomials

T. Kim,1 A. Bayad,2 and Y.-H. Kim1

1Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
2Département de Mathématiques, Université d'Evry Val d'Essonne, Boulevard François Mitterrand, 91025 Evry Cedex, France

Received 6 December 2010; Accepted 15 January 2011

Academic Editor: Vijay Gupta

Copyright © 2011 T. Kim 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 weighted 𝑞 -Bernstein polynomials related to the weighted 𝑞 -Bernoulli numbers and polynomials by using 𝑝 -adic 𝑞 -integral on ℤ 𝑝 .