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On ð ‘ -Adic Analogue of ð ‘ž -Bernstein Polynomials and Related Integrals

Author

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  • T. Kim
  • J. Choi
  • Y. H. Kim
  • L. C. Jang

Abstract

Recently, Kim's work (in press) introduced ð ‘ž -Bernstein polynomials which are different Phillips' ð ‘ž -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 ð ‘ž -Bernstein polynomials to express the ð ‘ -adic ð ‘ž -integral of these polynomials on ℤ ð ‘ associated with Carlitz's ð ‘ž -Bernoulli numbers and polynomials. Finally, we also derive some relations on the ð ‘ -adic ð ‘ž -integral of the products of several type Kim's ð ‘ž -Bernstein polynomials and the powers of them on ℤ ð ‘ .

Suggested Citation

  • T. Kim & J. Choi & Y. H. Kim & L. C. Jang, 2010. "On ð ‘ -Adic Analogue of ð ‘ž -Bernstein Polynomials and Related Integrals," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-9, January.
    • Handle: RePEc:hin:jnddns:179430
    DOI: 10.1155/2010/179430
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