# Some fixed point theorems for multifunctions with applications in game theory

- Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1985

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topBūi Cong Cuōng. Some fixed point theorems for multifunctions with applications in game theory. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1985. <http://eudml.org/doc/268400>.

@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 -

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