Some fixed point theorems for multifunctions with applications in game theory

@book{BūiCongCuōng1985,
abstract = {IntroductionThe main result of this paper is concerned with the conditions which guarantee that a multifunction $f: C → 2^X$ 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.},
author = {Būi Cong Cuōng},
keywords = {semicontinuous multifunctions; fixed point theorems},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Some fixed point theorems for multifunctions with applications in game theory},
url = {http://eudml.org/doc/268400},
year = {1985},
}

TY - BOOK
AU - Būi Cong Cuōng
TI - Some fixed point theorems for multifunctions with applications in game theory
PY - 1985
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - IntroductionThe main result of this paper is concerned with the conditions which guarantee that a multifunction $f: C → 2^X$ 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.
LA - eng
KW - semicontinuous multifunctions; fixed point theorems
UR - http://eudml.org/doc/268400
ER -