Coincidence theorems for families of multimaps and their applications to equilibrium problems
type: Item
instance of: scholarly article
title: Coincidence theorems for families of multimaps and their applications to equilibrium problems
zbMATH Open document ID: 1023.54032
DOI: 10.1155/S1085337503210034
author: Lai-Jiu Lin
author: Hsin I Chen
published in: Abstract and Applied Analysis
publication date: 2003-03-17T00:00:00Z
full work available at URL: https://eudml.org/doc/50385
review text: Let \(\{X_i\}_{i\in I}\), \(\{Y_j\}_{j\in J}\) be two families of convex sets each in a Hausdorff locally convex topological vector space and \(\{H_j:X=\prod_{i\in I} X_i\multimap Y_j\}_{j\in J}\), \(\{T_i:Y=\prod_{j\in J} Y_j\multimap X_i\}_{i\in I}\) be two families of multimaps. The paper is primarily concerned with the study of the existence of some coincidence points for the multimaps \(H=\prod_{j\in J}H_j\) and \(T=\prod_{i\in I}T_i\). Using some selection theorems and fixed point theorems the authors establish, under various conditions, several coincidence theorems for \(H\) and \(T\). In the last part of the paper the authors study the equilibrium problem with \(m\) families of players and \(2m\) families of constraints on strategy sets. Applying the coincidence theorems obtained in the first part the authors establish various existence theorems of equilibria of this problem and existence theorems of equilibria of abstract economics with two families of players.
reviewed by: Mircea Balaj
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 91A07
Mathematics Subject Classification ID: 46N10
zbMATH DE Number: 1883749
zbMATH Keywords: coincidence theorem
zbMATH Keywords: selection
zbMATH Keywords: fixed point
zbMATH Keywords: equilibrium problem
zbMATH Keywords: abstract economic problem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1883749