ON THE APPROXIMATION OF ANALYTIC FUNCTIONS BY THE q-BERNSTEIN POLYNOMIALS IN THE CASE
نویسندگان
چکیده
Abstract. Since for q > 1, the q-Bernstein polynomials Bn,q are not positive linear operators on C[0, 1], the investigation of their convergence properties turns out to be much more difficult than that in the case 0 < q < 1. In this paper, new results on the approximation of continuous functions by the q-Bernstein polynomials in the case q > 1 are presented. It is shown that if f ∈ C[0, 1] and admits an analytic continuation f(z) into {z : |z| < a}, then Bn,q(f ; z) → f(z) as n → ∞, uniformly on any compact set in {z : |z| < a}.
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