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On the Yosida approximation of operators

Published online by Cambridge University Press:  12 July 2007

Jean-Paul Penot  and
Robert Ratsimahalo
Jean-Paul Penot
Affiliation:
Laboratoire de Mathématiques Appliquées UPRES-A 5033 CNRS, Université de Pau et des Pays de l'Adour, Av. de l'Université, 64000 Pau, France ([email protected])
Robert Ratsimahalo
Affiliation:
Laboratoire de Mathématiques Appliquées UPRES-A 5033 CNRS, Université de Pau et des Pays de l'Adour, Av. de l'Université, 64000 Pau, France ([email protected])
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Abstract

A generalized Yosida approximation of monotone (and non-monotone) operators in Banach space is introduced. It uses a general potential that is not necessarily the square of the norm. It is therefore advisable to use it in cases where some other more convenient potentials are available, such as in Lp-spaces. As an illustration, the case of Nemyckii operators is considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 4 , August 2001 , pp. 945 - 966
Copyright
Copyright © Royal Society of Edinburgh 2001

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