Proceedings of the American Mathematical Society

Author(s): J. Berkovits; M. Miettunen
Journal: Proc. Amer. Math. Soc. 136 (2008), 3467-3476.
MSC (2000): Primary 47H11, 47H05
Posted: May 19, 2008
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Abstract: We consider the topological degree theory for maximal monotone perturbations of mappings of class

originally introduced by F. Browder in 1983. In the original construction it is implicitly assumed that the maximal monotone part is at least densely defined. The construction itself remains valid without this assumption. However, for the proof of the uniqueness of the degree the assumption is crucial. We shall recall the construction of the degree and show how the stabilization of the degree can be obtained directly, thus avoiding a series of technical lemmas used by F. Browder. The main result of this paper is the proof for the uniqueness of the degree in the general case. We also discuss the class of admissible homotopies, which may be quite narrow in case the domain of the maximal monotone part is not densely defined.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47H11, 47H05

J. Berkovits
Affiliation: Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014 Oulu, Finland

M. Miettunen
Affiliation: Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014 Oulu, Finland
Email: circus@mail.student.oulu.fi

DOI: 10.1090/S0002-9939-08-08998-3
PII: S 0002-9939(08)08998-3
Keywords: Uniqueness of the degree, maximal monotonicity, mappings of class $(S_+)$
Received by editor(s): June 5, 2006
Posted: May 19, 2008
Dedicated: In memory of Juha Berkovits, who passed away on 3 August 2007
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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ISSN 1088-6826 (e) ISSN 0002-9939 (p)

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