Well-posedness by perturbations of mixed variational inequalities in Banach spaces. (English) Zbl 1177.49018

The authors start with a short but rich in content introduction to different existing kinds of well-posedness followed by some remarks on later used analysis (e.g. monotone mappings, coerciveness, well-positioned sets, measure of compactness, uniformly convex Banach space). Then three new metric characterizations of the authors’ (to mixed variational inequalities) generalized concept of well-posedness by perturbations are explained and proved. Examples are included. The last two sections contain connections between well-posedness by perturbations of mixed variational inequality problems and corresponding inclusion or corresponding fixed point problems. With respect to fixed point problems some results of the authors in their paper in [J. Glob. Optim. 41, No. 1, 117–133 (2008; Zbl 1149.49009)] are generalized.


49J40 Variational inequalities
90C48 Programming in abstract spaces
90C31 Sensitivity, stability, parametric optimization
49J53 Set-valued and variational analysis
47H10 Fixed-point theorems


Zbl 1149.49009
Full Text: DOI


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