Openness Stability and Implicit Multifunction Theorems. Applications to Variational Systems

Details Openness Stability and Implicit Multifunction Theorems. Applications to Variational Systems Openness Stability and Implicit Multifunction Theorems. Applications to Variational Systems

2011-02-02

arxiv.org/abs/1102.0415v2

Nonlinear Analysis: TMA, Volume 75, Issue 3, 2012, Pages 1246-1259

Mathematics

Functional Analysis

21 pages

Scientific paper

10.1016/j.na.2011.02.019

In this paper we aim to present two general results regarding, on one hand, the openness stability of set-valued maps and, on the other hand, the metric regularity behavior of the implicit multifunction related to a generalized variational system. Then, these results are applied in order to obtain, in a natural way, and in a widely studied case, several relations between the metric regularity moduli of the ?eld maps de?ning the variational system and the solution map. Our approach allows us to complete and extend several very recent results in literature.

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