## Abstract and Applied Analysis

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

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 150975, 11 pages.

Dates
First available in Project Euclid: 12 August 2011

https://projecteuclid.org/euclid.aaa/1313170946

Digital Object Identifier
doi:10.1155/2010/150975

Mathematical Reviews number (MathSciNet)
MR2754202

Zentralblatt MATH identifier
1208.11029

#### Citation

Kim, T.; Choi, J.; Kim, Y. H. $q$ -Bernstein Polynomials Associated with $q$ -Stirling Numbers and Carlitz's $q$ -Bernoulli Numbers. Abstr. Appl. Anal. 2010 (2010), Article ID 150975, 11 pages. doi:10.1155/2010/150975. https://projecteuclid.org/euclid.aaa/1313170946