×

Continuous selection theorems in generalized convex spaces: Revisited. (English) Zbl 1244.54047

It is exhibited that 15 selection theorems for multifunctions in various convex spaces that appeared after 1999 can be easily deduced from a former result by the author [Numer. Funct. Anal. Optimization 20, No. 5–6, 567–583 (1999; Zbl 0931.54017)] with slight modifications. Such selection theorems are applicable to fixed point theory of multifunctions.

MSC:

54C65 Selections in general topology
47H04 Set-valued operators
47H10 Fixed-point theorems
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
46A55 Convex sets in topological linear spaces; Choquet theory
52A07 Convex sets in topological vector spaces (aspects of convex geometry)
54C60 Set-valued maps in general topology
54H25 Fixed-point and coincidence theorems (topological aspects)
55M20 Fixed points and coincidences in algebraic topology

Citations:

Zbl 0931.54017
PDFBibTeX XMLCite