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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 {\it 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 Continuous selections 52A01 Axiomatic and generalized geometric convexity 54C60 Set-valued maps (general topology) 26E25 Set-valued real functions
##### Keywords:
fixed-point; equilibrium; generalized convexity
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