Generic stability and essential components of generalized KKM points and applications
type: Item
instance of: scholarly article
title: Generic stability and essential components of generalized KKM points and applications
zbMATH Open document ID: 1229.58016
author: Phan Quoc Khanh
author: Nguyen Hong Quan
published in: Journal of Optimization Theory and Applications
publication date: 2011-05-11T00:00:00Z
review text: The authors present generic essentialness and essential components for generalized KKM points (see e.g. [\textit{P. Q. Khanh, N. H. Quan} and \textit{J.-C. Yao}, Nonlinear Anal., Theory Methods Appl. 71, No. 3--4, A, 1227--1234 (2009; Zbl 1176.47041)]) and apply them to solutions of variational inclusions and maximal elements. The definitions of a generalized KKM mapping with respect to a multivalued mapping \(T\) (\(T\)-KKM mapping in short) and \(T\)-KKM points are proposed. The authors prove generic stability: the set of essential points of a KKM-point map is a dense residual subset of a Hausdorff metric space of \(T\)-KKM maps. The existence of essential components of sets of \(T\)-KKM points is considered. From applications to solutions of variational inclusions the existence of essential components of Nash equilibria and Pareto efficient points is derived.
Mathematics Subject Classification ID: 58E17
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 91A06
Mathematics Subject Classification ID: 91A10
zbMATH DE Number: 5886728
zbMATH Keywords: KKM mapping
zbMATH Keywords: T-KKM point
zbMATH Keywords: generic stability
zbMATH Keywords: essential component
zbMATH Keywords: variational inclusion
zbMATH Keywords: maximal element
zbMATH Keywords: Nash equilibria
zbMATH Keywords: Pareto efficiency
zbMATH Keywords: quasi-optimization
MaRDI profile type: Publication
full work available at URL: s10957-010-9764-4
OpenAlex ID: W1987253423
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DOI: 10.1007/S10957-010-9764-4
description: scientific article; zbMATH DE number 5886728