Weighted approximation by Bernstein quasi-interpolants for functions with singularities

Abstract

We introduce a new type of modified Bernstein quasi-interpolants, which can be used to approximate functions with singularities. We establish direct, inverse, and equivalent theorems of the weighted approximation of this modified quasi-interpolants. Some classical results on approximation of continuous functions are generalized to the weighted approximation of functions with singularities.

Keywords

Quasi-interpolants / function with singularities / Bernstein operator / weighted approximation / equivalent theorem

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