Abstract and Applied Analysis
Volume 2011 (2011), Article ID 649248, 10 pages
http://dx.doi.org/10.1155/2011/649248
Research Article

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

Serkan Araci,1 Dilek Erdal,1 and Jong Jin Seo2

1Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, 27310 Gaziantep, Turkey
2Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea

Received 31 March 2011; Revised 25 June 2011; Accepted 18 July 2011

Academic Editor: Toka Diagana

Copyright © 2011 Serkan Araci 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 consider weighted 𝑞 -Genocchi numbers and polynomials. We investigated some interesting properties of the weighted 𝑞 -Genocchi numbers related to weighted 𝑞 -Bernstein polynomials by using fermionic 𝑝 -adic integrals on ℤ 𝑝 .