Abstract and Applied Analysis
Volume 2010 (2010), Article ID 952384, 15 pages
Research Article

On q-Euler Numbers Related to the Modified q-Bernstein Polynomials

1Department of Mathematics, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea
2National Institute for Mathematical Sciences, Doryong-dong, Yuseong-gu, Daejeon 305-340, Republic of Korea
3Division of General Education-Mathematics, Kwangwoon University, Seoul, 139-701, Republic of Korea

Received 19 July 2010; Accepted 27 August 2010

Academic Editor: Douglas Robert Anderson

Copyright © 2010 Min-Soo 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.


We consider q-Euler numbers, polynomials, and q-Stirling numbers of first and second kinds. Finally, we investigate some interesting properties of the modified q-Bernstein polynomials related to q-Euler numbers and q-Stirling numbers by using fermionic p-adic integrals on p.