Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 864247, 12 pages
doi:10.1155/2010/864247
Research Article

On the Fermionic 𝑝 -adic Integral Representation of Bernstein Polynomials Associated with Euler Numbers and Polynomials

T. Kim,1 J. Choi,1 Y. H. Kim,1 and C. S. Ryoo2

1Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
2Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea

Received 30 August 2010; Accepted 3 December 2010

Academic Editor: Paolo E. Ricci

Copyright © 2010 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

The purpose of this paper is to give some properties of several Bernstein type polynomials to represent the fermionic 𝑝 -adic integral on ℤ 𝑝 . From these properties, we derive some interesting identities on the Euler numbers and polynomials.