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

الملخص EN

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.