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Some fixed point theorems for concentrative mappings between locally convex linear topological spaces. (English) Zbl 0874.47035

The author proves a Leray-Schauder-type alternative for continuous operators on closed convex subsets of locally convex spaces which are condensing with respect to a generating family of seminorms. The abstract result is then applied to a fixed point problem on the locally convex space of continuous vector functions over the semi-axis, equipped with the usual family of “exhaustive” seminorms.

MSC:

47H10 Fixed-point theorems
47J25 Iterative procedures involving nonlinear operators
46A04 Locally convex Fréchet spaces and (DF)-spaces
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