Inverse of the Sum of Set-Valued Mappings and Applications

In this article, we develop results on the behavior of fixed points sets of set-valued pseudo-contraction mappings. Then, we investigate the notions related to the Aubin property and make use of connections between the two involved set-valued nonnecessarily Lipschitzian mappings to obtain results on...

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Bibliographic Details
Published in:Numerical functional analysis and optimization 2017-02, Vol.38 (2), p.139-159
Main Authors: Alleche, Boualem, Rădulescu, Vicenţiu D.
Format: Article
Language:English
Subjects:
Aubin property
Convergence
fixed point
Functional analysis
Inclusions
Inverse
Joints
Mapping
Mathematical models
Optimization
proximal convergence
pseudo-Lipschitzian
Sensitivity analysis
set-valued mapping
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Summary:In this article, we develop results on the behavior of fixed points sets of set-valued pseudo-contraction mappings. Then, we investigate the notions related to the Aubin property and make use of connections between the two involved set-valued nonnecessarily Lipschitzian mappings to obtain results on the inverse of their sum similar to those in the literature generalizing Lyusternik and Graves theorems. By proximal convergence, we apply our results to the sensitivity analysis of variational inclusions.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2016.1277741