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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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/179430 |
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| author | T. Kim J. Choi Y. H. Kim L. C. Jang |
| author_facet | T. Kim J. Choi Y. H. Kim L. C. Jang |
| author_sort | T. Kim |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5ba0c6e8a4514d6cb87e9f6bf803191c |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-5ba0c6e8a4514d6cb87e9f6bf803191c2025-02-03T05:52:09ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/179430179430On 𝑝-Adic Analogue of 𝑞-Bernstein Polynomials and Related IntegralsT. Kim0J. Choi1Y. H. Kim2L. C. Jang3Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of KoreaDivision of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of KoreaDivision of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of KoreaDepartment of Mathematics and Computer Science, KonKuk University, Chungju 380-701, Republic of KoreaRecently, 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.http://dx.doi.org/10.1155/2010/179430 |
| spellingShingle | T. Kim J. Choi Y. H. Kim L. C. Jang On 𝑝-Adic Analogue of 𝑞-Bernstein Polynomials and Related Integrals Discrete Dynamics in Nature and Society |
| title | On 𝑝-Adic Analogue of 𝑞-Bernstein Polynomials and Related Integrals |
| title_full | On 𝑝-Adic Analogue of 𝑞-Bernstein Polynomials and Related Integrals |
| title_fullStr | On 𝑝-Adic Analogue of 𝑞-Bernstein Polynomials and Related Integrals |
| title_full_unstemmed | On 𝑝-Adic Analogue of 𝑞-Bernstein Polynomials and Related Integrals |
| title_short | On 𝑝-Adic Analogue of 𝑞-Bernstein Polynomials and Related Integrals |
| title_sort | on 𝑝 adic analogue of 𝑞 bernstein polynomials and related integrals |
| url | http://dx.doi.org/10.1155/2010/179430 |
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