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Transactions of the American Mathematical Society

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A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact mappings


Authors: W. V. Petryshyn and P. M. Fitzpatrick
Journal: Trans. Amer. Math. Soc. 194 (1974), 1-25
MSC: Primary 47H11; Secondary 47H04, 47H10
DOI: https://doi.org/10.1090/S0002-9947-1974-2478129-5
MathSciNet review: 2478129
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Abstract: We define and study the properties of a topological degree for ultimately compact, multivalued vector fields defined on the closures of open subsets of certain locally convex topological vector spaces. In addition to compact mappings, the class of ultimately compact mappings includes condensing mappings, generalized condensing mappings, perturbations of compact mappings by certain Lipschitz-type mappings, and others. Using this degree we obtain fixed point theorems and mapping theorems.


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DOI: https://doi.org/10.1090/S0002-9947-1974-2478129-5
Article copyright: © Copyright 1974 American Mathematical Society

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