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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.
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