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Smoothness properties of modified Bernstein-Kantorovich operators. (English) Zbl 1337.41012

Summary: In this article, we consider modified Bernstein-Kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ones classically used. We obtain a simultaneous approximation result for our operators. Also, we prove two direct approximation results via the usual second-order modulus of smoothness and the second-order Ditzian-Totik modulus of smoothness, respectively. Finally, some graphical illustrations are provided.

MSC:

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