Well-posedness by perturbations of generalized mixed variational inequalities in Banach spaces
type: Item
instance of: scholarly article
title: Well-posedness by perturbations of generalized mixed variational inequalities in Banach spaces
zbMATH Open document ID: 1242.49014
DOI: 10.1155/2012/194509
author: L. C. Ceng
author: Ching-Feng Wen
published in: Journal of Applied Mathematics
publication date: 2012-04-04T00:00:00Z
review text: Summary: We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is also proven that, under suitable conditions, the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the well-posedness by perturbations of the corresponding inclusion problem and a corresponding fixed point problem. Furthermore, we derive some conditions under which the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the existence and uniqueness of its solution.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 49J27
zbMATH DE Number: 6021648
zbMATH Keywords: well-posedness by perturbations
zbMATH Keywords: generalized mixed variational inequalities
zbMATH Keywords: fixed-point problem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/194509
OpenAlex ID: W2005056276
Wikidata QID: Q58906349
cites work: On the stability of the functional optimization problem
cites work: Well-posedness criteria in optimization with application to the calculus of variations
cites work: Extended well-posedness of optimization problems
cites work: A characterization of tyhonov well-posedness for minimum problems, with applications to variational inequalities(∗)
cites work: Metrically well-set minimization problems
cites work: Well-posed optimization problems
cites work: Extended and strongly extended well-posedness of set-valued optimization problems
cites work: Well-posedness for mixed quasivariational-like inequalities
cites work: Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems
cites work: Well-posedness by perturbations of mixed variational inequalities in Banach spaces
cites work: Well-posedness of generalized mixed variational inequalities, inclusion problems and fixed-point problems
cites work: Well-posedness for optimization problems with constraints defined by variational inequalities having a unique solution
cites work: Q4412356
cites work: Q3668367
cites work: Approximations and well-posedness in multicriteria games
cites work: Q4848726
cites work: On the Tikhonov well-posedness of concave games and Cournot oligopoly games
cites work: Well-posedness for equilibrium problems and for optimization problems with equilibrium constraints
cites work: Well-posedness by perturbations of variational problems
cites work: Q4485612
cites work: Unified approaches to well-posedness with some applications
cites work: Iterative method for set-valued mixed quasi-variational inequalities in a Banach space
cites work: Existence of solutions of generalized vector variational inequalities in reflexive Banach spaces
cites work: Q3414022
cites work: Q4089219
cites work: Multi-valued contraction mappings
cites work: Q5541833
cites work: Q3706043
cites work: Well-positioned closed convex sets and well-positioned closed convex functions
cites work: Strict feasibility of variational inequalities in reflexive Banach spaces
cites work: On the Subdifferentiability of Convex Functions
cites work: Q3999276
cites work: Q4022917
DBLP publication ID: journals/jam/CengW12
description: scientific article; zbMATH DE number 6021648