Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Author:

Moldovan Camelia LilianaORCID,Păltănea RaduORCID

Abstract

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

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5. On variation-diminishing Schoenberg operators: New quantitative statements;Beutel;Monogr. Acad. Cienc. Zaragoza,2002

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