We construct the analogues of Bernstein polynomials on the set Js of s finitely many intervals. Two cases are considered: first when there are no restrictions on Js, and then when Js has a so-called T-polynomial. On such sets we define approximating operators resembling the classic Bernstein polynomials. Reproducing and interpolation properties as well as estimates for the rate of convergence are given.
CITATION STYLE
Szabados, J. (2017). Bernstein-type polynomials on several intervals. In Springer Optimization and Its Applications (Vol. 117, pp. 301–315). Springer International Publishing. https://doi.org/10.1007/978-3-319-49242-1_14
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