q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients

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q-Extensions of Some Relationships Between the Bernoulli and Euler Polynomials (2011, background): “([16-22] and [23]), Ozden and Simsek [26], Ryoo et al.”
Note on the Euler Numbers and Polynomials (2008, background): “n=0 En t n! , for |t| ≤ π, (see [1-31]), are known as the Euler numbers.”
Some Generalizations and Basic (or q-) Extensions of the Bernoulli, Euler (2011, unknown): “( [26], [27], [28], [29], [31], [32], [33], [34], [36] and [37]), Luo and Srivastava [54], Ozden and Simsek [57], Ryoo et al.”
A note on q-Bernstein polynomials (2010, background): “In the last decade some new generalizations of well known positive linear operators based on q-integers were introduced and studied by several authors(see [1-21]).”