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Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials

Author

Listed:
  • Taekyun Kim

    (Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea)

  • Dae San Kim

    (Department of Mathematics, Sogang University, Seoul 121-742, Korea)

Abstract

In recent years, intensive studies on degenerate versions of various special numbers and polynomials have been done by means of generating functions, combinatorial methods, umbral calculus, p -adic analysis and differential equations. The degenerate Bernstein polynomials and operators were recently introduced as degenerate versions of the classical Bernstein polynomials and operators. Herein, we firstly derive some of their basic properties. Secondly, we explore some properties of the degenerate Euler numbers and polynomials and also their relations with the degenerate Bernstein polynomials.

Suggested Citation

  • Taekyun Kim & Dae San Kim, 2019. "Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials," Mathematics, MDPI, vol. 7(1), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:47-:d:195011
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    References listed on IDEAS

    as
    1. A. Bayad & T. Kim & B. Lee & S.-H. Rim, 2011. "Some Identities on Bernstein Polynomials Associated with ð ‘ž -Euler Polynomials," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-10, April.
    2. Taekyun Kim, 2011. "Some Identities on the ð ‘ž -Integral Representation of the Product of Several ð ‘ž -Bernstein-Type Polynomials," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-11, December.
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