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On some classes of Bernstein type operators which preserve the global smoothness in the case of univariate functions. (English) Zbl 1101.41025
Summary: The aim of this paper is to describe the linear and positive operators which have the property of preservation of the global smoothness. We insist on the Bernstein and Stancu operators. We consider the case of univariate functions.
In order to show the preservation of global smoothness, we use the notions of modulus of continuity and $$K$$-functionals.
##### MSC:
 41A35 Approximation by operators (in particular, by integral operators) 41A36 Approximation by positive operators
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