A note on q-Bernstein polynomials
- 24 March 2011
- journal article
- Published by Pleiades Publishing Ltd in Russian Journal of Mathematical Physics
- Vol. 18 (1) , 73-82
- https://doi.org/10.1134/s1061920811010080
Abstract
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.Keywords
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