A note on q-Bernstein polynomials

By Taekyun Kim. 2010

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Recently, Simsek-Acikgoz [17] and Kim-Jang-Yi [9] have studied the q-extension of Bernstein polynomials. In the present paper, we suggest q-extensions of Bernstein polynomials of degree n which differ from the q-Bernstein polynomials of Simsek-Acikgoz [17] and Kim-Jang-Yi [9]. Using these q-Bernstein polynomials, we derive fermionic p-adic integral representations of several q-Bernstein-type polynomials. Finally, we investigate identities between q-Bernstein polynomials and q-Euler numbers.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/084070df5b1497dc0696b0d6f16f9d15ce6e4ed4