A family of univariate rational Bernstein operators

Authors:
Paula Piţul;Paul Sablonnière
Affiliations:
University of Duisburg-Essen, Forsthausweg 2, 47057-Duisburg, Germany;University of Duisburg-Essen, Forsthausweg 2, 47057-Duisburg, Germany and INSA, 20 avenue des Buttes de Coësmes, CS 14315, 35043-Rennes cedex, France
Venue:
Journal of Approximation Theory
Year:
2009

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Abstract

We define and study a new family of univariate rational Bernstein operators. They are positive operators exact on linear polynomials. Moreover, like classical polynomial Bernstein operators, they enjoy the traditional shape preserving properties and they are total variation diminishing. Finally, for a specific class of denominators, some convergence results are proved, in particular a Voronovskaja theorem, and some error bounds are given.