Abstract and Applied Analysis
Volume 2010 (2010), Article ID 150975, 11 pages
doi:10.1155/2010/150975
Research Article

𝑞 -Bernstein Polynomials Associated with 𝑞 -Stirling Numbers and Carlitz's 𝑞 -Bernoulli Numbers

T. Kim, J. Choi, and Y. H. Kim

Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea

Received 17 September 2010; Revised 10 December 2010; Accepted 28 December 2010

Academic Editor: Ferhan M. Atici

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

Recently, Kim (2011) introduced 𝑞 -Bernstein polynomials which are different 𝑞 -Bernstein polynomials of Phillips (1997). In this paper, we give a 𝑝 -adic 𝑞 -integral representation for 𝑞 -Bernstein type polynomials and investigate some interesting identities of 𝑞 -Bernstein type polynomials associated with 𝑞 -extensions of the binomial distribution, 𝑞 -Stirling numbers, and Carlitz's 𝑞 -Bernoulli numbers.