An axiomatic approach to a coincidence index for noncompact function pairs
Keywords
Degree theory, fixed point index, coincidence index, condensing operator, measure of noncompactnessAbstract
We prove that there is a coincidence index for the inclusion $F(x)\in\Phi(x)$ when $\Phi$ is convex-valued and satisfies certain compactness assumptions on countable sets. For $F$ we assume only that it provides a coincidence index for single-valued finite-dimensional maps (e.g. $F$ is a Vietoris map). For the special case $F={\rm id}$, the obtained fixed point index is defined if $\Phi$ is countably condensing; the assumptions in this case are even weaker than in [M. Väth, < i> Fixed point theorems and fixed point index for countably condensing maps< /i> , Topol. Methods Nonlinear Anal. < b> 13< /b> (1999), 341–363].Downloads
Published
2000-12-01
How to Cite
1.
VÄTH, Martin. An axiomatic approach to a coincidence index for noncompact function pairs. Topological Methods in Nonlinear Analysis. Online. 1 December 2000. Vol. 16, no. 2, pp. 307 - 338. [Accessed 28 March 2024].
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