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Continuous selection theorems in generalized convex spaces. (English) Zbl 0931.54017

Strongly continuous (i.e. having open fibers) multifunctions on compact or paracompact spaces with generalized convex values in \(G\)-spaces are considered. The concept of such \(G\)-spaces is the author’s very general nice extension of the generalized convexity in the spirit of R. Bielawski [J. Math. Anal. Appl. 127, No. 4, 155-171 (1987; Zbl 0638.52002)]. The existence of global or local continuous selections, fixed points and equilibria is investigated in the above framework. Large and exhaustive comparison with the existing results by Ben-El-Mechaiekh, Horváth, Kim, Yannelis and Prabhakar, Pasicki and many others is enclosed.

MSC:

54C65 Selections in general topology
52A01 Axiomatic and generalized convexity
54C60 Set-valued maps in general topology
26E25 Set-valued functions

Citations:

Zbl 0638.52002
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References:

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