Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

On the Yosida approximation of operators

Jean-Paul Penota1 and Robert Ratsimahaloa1

a1 Laboratoire de Mathématiques Appliquées UPRES-A 5033 CNRS, Université de Pau et des Pays de l'Adour, Av. de l'Université, 64000 Pau, France (jean-paul.penot@univ-pau.fr)

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.

(Received November 23 1999)

(Accepted May 18 2000)