Inverse of the Sum of Set-Valued Mappings and Applications. (1st February 2017)

• Record Type: Journal Article
• Authors: Alleche, Boualem; Rădulescu, Vicenţiu D.
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 2(2017)
• Page Start: 139
• Page End: 159
• Publication Date: 2017-02-01
• Subjects: Aubin property -- fixed point -- proximal convergence -- pseudo-Lipschitzian -- set-valued mapping; 49J53 -- 47J22 -- 49J40 -- 49K40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1277741
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: 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.