On p-Adic Analogue of q-Bernstein Polynomials and Related Integrals

Recently, Kim's work (in press) introduced q-Bernstein polynomials which are different Phillips' q-Bernstein polynomials introduced in the work by (Phillips, 1996; 1997). The purpose of this paper is to study some properties of several type Kim's q-Bernstein polynomials to express the...

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Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2010-01, Vol.2010 (1), p.92-100
Main Authors: Kim, T., Choi, J., Kim, Y. H., Jang, L. C.
Format: Article
Language:English
Subjects:
Computer science
Numbers
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Summary:Recently, Kim's work (in press) introduced q-Bernstein polynomials which are different Phillips' q-Bernstein polynomials introduced in the work by (Phillips, 1996; 1997). The purpose of this paper is to study some properties of several type Kim's q-Bernstein polynomials to express the p-adic q-integral of these polynomials on ℤp associated with Carlitz's q-Bernoulli numbers and polynomials. Finally, we also derive some relations on the p-adic q-integral of the products of several type Kim's q-Bernstein polynomials and the powers of them on ℤp.
ISSN:1026-0226
1607-887X
DOI:10.1155/2010/179430