Fixed point theorems and fixed point index for countably condensing maps
Keywords
Fixed point theorem, countably condensing operator, fixed point index, degree theory, measure of noncompactness, sequential measure of noncompactness, multivalued mapping, fundamental set, ultimately compact operator, Fredholm operator, positive operatorAbstract
It is proved that there exists a fixed point index theory for operators which are condensing on the countable subsets of the space only. Even weaker compactness assumptions on countable subsets suffice, e.g. conditions with respect to classes of measures of noncompactness, or if measures of noncompactness of countable noncompact sets are not preserved (not necessarily decreased). As an application, we prove a generalization of the Fredholm alternative.Downloads
Published
1999-06-01
How to Cite
1.
VÄTH, Martin. Fixed point theorems and fixed point index for countably condensing maps. Topological Methods in Nonlinear Analysis. Online. 1 June 1999. Vol. 13, no. 2, pp. 341 - 363. [Accessed 23 September 2024].
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