Generic uniqueness of equilibrium points
type: Item
instance of: scholarly article
title: Generic uniqueness of equilibrium points
zbMATH Open document ID: 1237.47062
author: Jian Yu
author: Dingtao Peng
author: Shuwen Xiang
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2011-10-17T00:00:00Z
review text: Let \(X\) a convex compact subset of a normed linear space \(E\). Denote by \(M\) the class of all \(f:X\times X\to \mathbb R\) fulfilling (i) \(x\mapsto f(x,y)\) is usc on \(X\), \(\forall y\in X\), (ii) \(y\mapsto f(x,y)\) is convex on \(X\), \(\forall x\in X\), (iii) \(f(x,x)\geq 0\), \(\forall x\in X\), (iv) \(f(x,y)+f(y,x)\leq 0\), \(\forall x,y\in X\), (v) \(\sup\{|f(x,y)|; x,y\in X\}< \infty\). {Theorem.} There exists a dense residual subset \(Q\) of \(M\) such that, for each \(f\in Q\), the set of equilibrium points for \(f\) is a singleton. A non-compact (modulo \(X\)) version of this result is also given by the perturbation of the couples \((f,A)\), where \(f\) is as before and \(A\) is a convex compact part of \(X\).
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 47H14
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 5959689
zbMATH Keywords: Hausdorff topological vector space
zbMATH Keywords: convex compact subset
zbMATH Keywords: binary function
zbMATH Keywords: equilibrium point
zbMATH Keywords: dense residual subset
zbMATH Keywords: Baire category
zbMATH Keywords: feasible set
zbMATH Keywords: usco map
MaRDI profile type: Publication
full work available at URL: j.na.2011.06.011
OpenAlex ID: W2057622585
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DOI: 10.1016/J.NA.2011.06.011
description: scientific article; zbMATH DE number 5959689