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

O’Regan, Donal

Nonlinear Anal., Theory Methods Appl. 27, No. 12, 1437-1446 (1996).

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.

Reviewer: J.Appell (Würzburg)

MSC:

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

Keywords:

exhaustive seminorms; Leray-Schauder-type alternative; continuous operators; closed convex subsets of locally convex spaces; condensing with respect to a generating family of seminorms; fixed point problem; space of continuous vector functions

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