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On the best convergence order of a new class of triangular summation operators. (English) Zbl 1156.41309

Summary: A new class of triangular summation operators based on the equidistant nodes is constructed. It is proved that this class of operators converges uniformly to arbitrary continuous functions with the period \(2\pi\) on the whole axis. Furthermore, the best approximation order and the highest convergence order are obtained. In contrast to certain operators constructed by Bernstein and O. Kis in the previous works, the convergence properties of the new operator constructed in this paper are superior.

MSC:

41A25 Rate of convergence, degree of approximation
41A55 Approximate quadratures
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