IntroductionThe main result of this paper is concerned with the conditions which guarantee that a multifunction defined on an arbitrary subset C of a topological vector space X admits a point x of C such that x∈f(x).First, we give some definitions and propositions which are associated with semicontinuous multifunctions (Part 1).Next, in Part 2, we present a global convergence criterion on variable dimension algorithms for finding an approximate solution of the equation x∈f(x), and then we consider some fixed point theorems for multifunctions defined in finite-dimensional spaces.Part 3 contains fixed point theorems for quasi upper semicontinuous multifunctions defined on arbitrary domains of topological vector spaces which generalize the theorems with boundary conditions.Part 4 is devoted to some fixed point theorems for strongly lower semicontinuous multifunctions and thus here we are first concerned with fixed point theorems under boundary conditions for this class of multi-functions.The last part shows how we can apply the results obtained to existence problem of equilibrium situations in the theory of non-cooperative games.
CONTENTSIntroduction..........................................................................................................51. Some classes of semicontinuous multifunctions...............................................52. A remark on the convergence of variable dimension algorithms.......................93. Some fixed point theorems.............................................................................154. Fixed point theorems for strongly lower semicontinuous multifunctions..........245. Some applications in game theory..................................................................29References.........................................................................................................34
@book{bwmeta1.element.zamlynska-155138a6-b463-4568-8480-751bd0931946,
author = {B\=ui Cong Cu\=ong},
title = {Some fixed point theorems for multifunctions with applications in game theory},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1985},
zbl = {0636.47042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-155138a6-b463-4568-8480-751bd0931946}
}
Būi Cong Cuōng. Some fixed point theorems for multifunctions with applications in game theory. GDML_Books (1985), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-155138a6-b463-4568-8480-751bd0931946/