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Approximation by \(k\)-th order modifications of Szász-Mirakyan operators. (English) Zbl 1389.41016

The authors introduce the \(k\)-th order Kantorovich-type modification of Szász-Mirakyan operators and study their approximation properties as the rate of convergence and simultaneous approximation. The explicit formulas of the moments up to order six are also given for the new operators and a quantitative Voronovskaya theorem for differentiated Szász-Mirakyan operators in weighted spaces is established.

MSC:

41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
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