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Bivariate approximation by algebraic and trigonometric blending functions. (English) Zbl 0618.41017

Some joint results due to C. Cottin, H. H. Gonska and the present authors on bivariate approximation by blending functions (pseudopolynomials) are presented without proof. The main conclusion is that the considered method for constructing algebraic and trigonometric blending approximants (a generalization of the Boolean sum operator method) leads to some ”perturbed” operators which are approximating in the larger space of so- called bivariate Bögel-continuous functions. Some results on the algebraic case were established by the present authors and H. H. Gonska [Bull. Aust. Math. Soc. 34, 53-64 (1986; Zbl 0595.41017)] while the trigonometric case is treated in a joint paper of the present authors and C. Cottin (A Korovkin-type theorem for generalizations polynomials, to appear). Also, a partial answer to a (still open) question is presented.

MSC:

41A35 Approximation by operators (in particular, by integral operators)
41A63 Multidimensional problems
42A10 Trigonometric approximation

Citations:

Zbl 0595.41017
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