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Modified Szász-Mirakjan-Kantorovich operators preserving linear functions. (English) Zbl 1175.41015

Summary: We introduce a modification of the Szász-Mirakjan-Kantorovich operators, which preserve the linear functions. This type of operator modification enables better error estimation on the interval \([1/2,+\infty)\) than the classical Szász-Mirakjan-Kantorovich operators. We also obtain a Voronovskaya-type theorem for these operators.

MSC:

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