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On the homotopy property of degree for multivalued noncompact maps

Published online by Cambridge University Press:  18 May 2009

J. R. L. Webb
J. R. L. Webb
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405
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Over the last few years, various extensions of the topological degree of a mapping have been made so as to include non-compact perturbations of the identity. One such extension, which employs compactness conditions, has been to the class of limit compact maps which were extensively studied by Sadovsky [7]. The class is a large one as it contains all compact mappings, contraction mappings and, more generally, condensing mappings. Sadovsky [7] gives a theory of degree for maps of the form I-f, where f is limit compact, and this was extended independently and with different methods by Petryshyn and Fitzpatrick [4] and the author [9] to allow f to be a multi-valued mapping. A refinement of the methods of [9] was given by Vanderbauwhede [8].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 125 - 130
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

1.Cellina, A. and Lasota, A., A new approach to the definition of topological degree for multi-valued mappings, Atti. Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Natur. 47 (1969), 434–440.Google Scholar
2.de Pascale, E. and Guzzardi, R., On the boundary values dependence for the topological degree of multi-valued noncompact maps, Boll. Un. Mat. Ital. 13-A (1976), 110–116.Google Scholar
3.Fitzpatrick, P. M. and Petryshyn, W. V., Fixed point theorems and the fixed point index for multivalued mappings in cones, J. London Math. Soc. (2) 12 (1975), 75–85.CrossRefGoogle Scholar
4.Fitzpatrick, P. M. and Petryshyn, W. V., A degree theory, fixed point theorems, and mapping theorems for multi-valued noncompact mappings, Trans. Amer. Math. Soc. 194 (1974), 1–25.Google Scholar
5.Kamke, E., Theory of sets (Dover, 1950).Google Scholar
6.Rudin, W., Functional analysis (McGraw-Hill, 1973).Google Scholar
7.Sadovsky, B. N., Limit compact and condensing operators (English translation), Russian Math. Surveys, 27, (1972), 85–155.CrossRefGoogle Scholar
8.Vanderbauwhede, A., On a modified degree theory for multi-valued mappings, Simon Stevin, 50 (1976–1977), 65–86.Google Scholar
9.Webb, J. R. L., On degree theory for multi-valued mappings and applications, Boll. Un. Mat. Ital. 9 (1974), 137–158.Google Scholar
10.Webb, J. R. L., On uniqueness of topological degree for set-valued mappings, Proc. Roy. Soc. Edinburgh, Sect. A 74 (1974–1975), 225–229.CrossRefGoogle Scholar