منابع مشابه
On the Convergence and Iterates of q-Bernstein Polynomials
The convergence properties of q-Bernstein polynomials are investigated. When q > 1 is fixed the generalized Bernstein polynomials Bnf of f , a one parameter family of Bernstein polynomials, converge to f as n → ∞ if f is a polynomial. It is proved that, if the parameter 0 < q < 1 is fixed, then Bnf → f if and only if f is linear. The iterates of Bnf are also considered. It is shown that B n f c...
متن کاملModified Bernstein Polynomials and Jacobi Polynomials in q-Calculus
We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the q-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in ]0, 1[. Numerous properties of the modified Bernstein Polynomials are extended to their q-analogues: simultaneous approximation, p...
متن کاملSome Identities on the q-Tangent Polynomials and Bernstein Polynomials
In this paper, we investigate some properties for the q-tangent numbers and polynomials. By using these properties, we give some interesting identities on the q-tangent polynomials and Bernstein polynomials. Throughout this paper, let p be a fixed odd prime number. The symbol, Zp, Qp and Cp denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic ...
متن کاملSome Identities on the Twisted (h, q)-Genocchi Numbers and Polynomials Associated with q-Bernstein Polynomials
Let p be a fixed odd prime number. Throughout this paper, we always make use of the following notations: Z denotes the ring of rational integers, Zp denotes the ring of padic rational integer, Qp denotes the ring of p-adic rational numbers, and Cp denotes the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N {0}. Let Cpn {ζ | ζpn 1} be the cyclic g...
متن کاملSOME IDENTITIES ON THE BERNSTEIN AND q-GENOCCHI POLYNOMIALS
Let p be a fixed odd prime number. Throughout this paper, Zp, Qp and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and N = N ∪ {0}. The p-adic norm is normally defined by |p|p = 1/p. As an indeterminate, we assume that q ∈ Cp with |1 − q|p < 1 (see [1-43]...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2003
ISSN: 0021-9045
DOI: 10.1016/s0021-9045(03)00104-7