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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.
Būi 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 -