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Lefschetz fixed point theory for compact absorbing contractive admissible maps. (English) Zbl 1206.47048

The authors use a characterization of a Fréchet space as a proximal limit of Banach spaces (\(E=\lim_\leftarrow E_n\)), and present several Lefschetz-type fixed point results for compact absorbing contractive admissible maps in a Fréchet space \(E\) under suitable assumptions on corresponding maps in Banach spaces \(E_n\).
The last part of the paper (Section 3) contains analogs of results from Section 2 for condensing maps and for condensing maps with compact attractor.

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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