scholarly journals Maximal elements and equilibria of generalized games for𝒰-majorized and condensing correspondences

1999 ◽  
Vol 22 (1) ◽  
pp. 179-189 ◽  
Author(s):  
George Xian-Zhi Yuan ◽  
E. Tarafdar
Keyword(s):  
Existence Theorem ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Topological Vector Spaces ◽  
New Type ◽  
Generalized Games ◽  
Locally Convex ◽  
Qualitative Games

In this paper, we first give an existence theorem of maximal elements for a new type of preference correspondences which are𝒰-majorized. Then some existence theorems for compact (resp., non-compact) qualitative games and generalized games in which the constraint or preference correspondences are𝒰-majorized (resp.,Ψ-condensing) are obtained in locally convex topological vector spaces.

scholarly journals Equilibrium points of random generalized games

1998 ◽  
Vol 21 (4) ◽  
pp. 791-800 ◽  
Author(s):  
E. Tarafdar ◽  
Xian-Zhi Yuan
Keyword(s):  
Existence Theorem ◽  
Existence Theorems ◽  
Equilibrium Points ◽  
Lower Semicontinuous ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Equilibrium Existence ◽  
Topological Vector Spaces ◽  
Generalized Games ◽  
Random Games

In this paper, the concepts of random maximal elements, random equilibria and random generalized games are described. Secondly by measurable selection theorem, some existence theorems of random maximal elements forLc-majorized correspondences are obtained. Then we prove existence theorems of random equilibria for non-compact one-person random games. Finally, a random equilibrium existence theorem for non-compact random generalized games (resp., random abstract economics) in topological vector spaces and a random equilibrium existence theorem of non-compact random games in locally convex topological vector spaces in which the constraint mappings are lower semicontinuous with countable number of players (resp., agents) are given. Our results are stochastic versions of corresponding results in the recent literatures.

scholarly journals Maximal elements and equilibria for u-majorised preferences

1994 ◽  
Vol 49 (1) ◽  
pp. 47-54 ◽  
Author(s):  
Kok-Keong Tan ◽  
Xian-Zhi Yuan
Keyword(s):  
Existence Theorem ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Topological Vector Spaces ◽  
Qualitative Game ◽  
New Type ◽  
General Existence ◽  
Locally Convex

The purpose of this note is to give a general existence theorem for maximal elements for a new type of preference correspondences which are u-majorised. As an application, an existence theorem of equilibria for a qualitative game is obtained in which the preferences are u-majorised with an arbitrary (countable or uncountable) set of players and without compactness assumption on their domains in Hausdorff locally convex topological vector spaces.

A minimax inequality with applications to existence of equilibrium points

1993 ◽  
Vol 47 (3) ◽  
pp. 483-503 ◽  
Author(s):  
Kok-Keong Tan ◽  
Zian-Zhi Yuan
Keyword(s):  
Existence Theorems ◽  
Equilibrium Points ◽  
Vector Spaces ◽  
Minimax Inequality ◽  
Approximation Technique ◽  
Maximal Elements ◽  
Equilibrium Existence ◽  
Topological Vector Spaces ◽  
Person Game ◽  
Element Theorem

A new minimax inequality is first proved. As a consequence, five equivalent fixed point theorems are formulated. Next a theorem concerning the existence of maximal elements for an Lc-majorised correspondence is obtained. By the maximal element theorem, existence theorems of equilibrium points for a non-compact one-person game and for a non-compact qualitative game with Lc-majorised correspondences are given. Using the latter result and employing an “approximation” technique used by Tulcea, we deduce equilibrium existence theorems for a non-compact generalised game with LC correspondences in topological vector spaces and in locally convex topological vector spaces. Our results generalise the corresponding results due to Border, Borglin-Keiding, Chang, Ding-Kim-Tan, Ding-Tan, Shafer-Sonnenschein, Shih-Tan, Toussaint, Tulcea and Yannelis-Prabhakar.

scholarly journals Existence of solutions for generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 909-916 ◽  
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Nonlinear Vector ◽  
Locally Convex

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variational- like inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalized mixed quasi-variational-like inequalities and so on. By means of fixed point theorem, we obtain existence theorem of solutions to the class of generalized nonlinear vector quasi-variational-like inequalities in the setting of locally convex topological vector spaces.

scholarly journals A coincidence theorem in topological vector spaces

1986 ◽  
Vol 33 (3) ◽  
pp. 373-382 ◽  
Author(s):  
Olga Hadžić
Keyword(s):  
Vector Spaces ◽  
Maximal Elements ◽  
Topological Vector Spaces ◽  
Coincidence Theorem ◽  
Locally Convex ◽  
Special Case

In this paper we prove a coincidence theorem in not necessarily locally convex topological vector spaces, which contains, as a special case, a coincidence theorem proved by Felix Browder. As an application, a result about the existence of maximal elements is obtained.

scholarly journals Fixed Points, Maximal Elements and Equilibria of Generalized Games in Abstract Convex Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Yan-Mei Du
Keyword(s):  
Fixed Point ◽  
Convex Space ◽  
Fixed Point Theorems ◽  
Recent Literature ◽  
Existence Theorems ◽  
Maximal Elements ◽  
Abstract Convex Space ◽  
Generalized Games ◽  
Set Valued Mappings ◽  
Qualitative Games

We firstly prove some new fixed point theorems for set-valued mappings in noncompact abstract convex space. Next, two existence theorems of maximal elements for class of𝒜C,θmapping and𝒜C,θ-majorized mapping are obtained. As in applications, we establish new equilibria existence theorems for qualitative games and generalized games. Our theorems improve and generalize the most known results in recent literature.

scholarly journals On the existence of solutions for vector quasiequilibrium problems

2019 ◽  
Vol 15 (3) ◽  
pp. 48
Author(s):  
Nguyen Xuan Hai ◽  
Nguyen Van Hung
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Quasiequilibrium Problems ◽  
Solution Sets ◽  
Topological Vector Spaces ◽  
Vector Quasiequilibrium Problems ◽  
Locally Convex

In this paper, we establish some existence theorems for vector quasiequilibrium problems in real locally convex Hausdorff topological vector spaces by using Kakutani-Fan-Glicksberg fixed-point theorem. Moreover, we also discuss the closedness of the solution sets for these problems. The results presented in the paper are new and improve some main results in the literature.

scholarly journals Equilibria of generalized games withL-majorized correspondences

1994 ◽  
Vol 17 (4) ◽  
pp. 783-790 ◽  
Author(s):  
Xie Ping Ding ◽  
Won Kyu Kim ◽  
Kok-Keong Tan
Keyword(s):  
Existence Theorems ◽  
Vector Spaces ◽  
Equilibrium Existence ◽  
Topological Vector Spaces ◽  
Generalized Games

In this paper, we shall prove three equilibrium existence theorems for generalized games in Hausdorff topological vector spaces.

Finite dimensional locally convex cones

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5111-5116
Author(s):  
Davood Ayaseha
Keyword(s):  
Finite Dimension ◽  
Convex Cones ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Euclidean Topology ◽  
Finite Dimensional ◽  
Dimensional Cone ◽  
Locally Convex Cones ◽  
Locally Convex ◽  
Special Case

We study the locally convex cones which have finite dimension. We introduce the Euclidean convex quasiuniform structure on a finite dimensional cone. In special case of finite dimensional locally convex topological vector spaces, the symmetric topology induced by the Euclidean convex quasiuniform structure reduces to the known concept of Euclidean topology. We prove that the dual of a finite dimensional cone endowed with the Euclidean convex quasiuniform structure is identical with it?s algebraic dual.

scholarly journals ULTRAMETRIC AND NON-LOCALLY CONVEX ANALOGUES OF THE GENERAL CURVE LEMMA OF CONVENIENT DIFFERENTIAL CALCULUS

2008 ◽  
Vol 50 (2) ◽  
pp. 271-288
Author(s):  
HELGE GLÖCKNER
Keyword(s):  
Differential Calculus ◽  
Vector Spaces ◽  
Local Convexity ◽  
Topological Vector Spaces ◽  
Infinite Dimensional ◽  
General Curve ◽  
Infinite Dimensional Analysis ◽  
Locally Convex ◽  
Differentiability Properties ◽  
Made In

AbstractThe General Curve Lemma is a tool of Infinite-Dimensional Analysis that enables refined studies of differentiability properties of maps between real locally convex spaces to be made. In this article, we generalize the General Curve Lemma in two ways. First, we remove the condition of local convexity in the real case. Second, we adapt the lemma to the case of curves in topological vector spaces over ultrametric fields.

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