Abstract
We construct the analogues of Bernstein polynomials on the set J s of s finitely many intervals. Two cases are considered: first when there are no restrictions on J s , and then when J s 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.
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2000 Mathematics Subject Classification
Dedicated to the memory of Professor Qazi Ibadur Rahman
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The research was supported by OTKA Grant No. K111742.
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Szabados, J. (2017). Bernstein-Type Polynomials on Several Intervals. In: Govil, N., Mohapatra, R., Qazi, M., Schmeisser, G. (eds) Progress in Approximation Theory and Applicable Complex Analysis. Springer Optimization and Its Applications, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-49242-1_14
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DOI: https://doi.org/10.1007/978-3-319-49242-1_14
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