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On conservative approximation by linear polynomial operators an extension of the Bernstein's operator |
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| Authors: | Francisco-Javier Muñoz-Delgado Victoriano Ramirez-González Paul Sablonnière |
| Institution: | 1. Departmento de Matemáticas, Universidad de Jaén, Escuela Politécnica Superior Avda, Madrid, 35, 23071, Jaén, Spain 2. Departamento de Matemática Aplicada Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain 3. Laboratorie LANS, Institut National des Sciences Appliquées, 20. avenue des Buttes de Co?smes, 35043, Rennes Cedex, France |
| Abstract: | In this work we study linear polynomial operators preserving some consecutive i-convexities and leaving invariant the polynomials up to a certain degree. First, we study the existence of an incom patibility between the conservation of certain i-convexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DeVore about the Bernstein's operator is extended. Finally, from these results a generalized Bernstein's operator is obtained. This work was supported by Junta de Andalucia. Grupo de investigación: Matemática Aplicada. Código: 1107 |
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