Abstract:Many approximation processes for multivariate real-valued functions are constructed on the basis of parametric extensions of univariate approximation operators. A parametric extension of a univariate operator with respect to the i/-th component is defined in such a way that it acts on a multivariate function as if all variables except of the i/-th one were fixed. We generalize this approach by introducing directional extensions of univariate operators, which are defined similarly as parametric extensions, but … Show more
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