Journal
SET-VALUED AND VARIATIONAL ANALYSIS
Volume 31, Issue 2, Pages -Publisher
SPRINGER
DOI: 10.1007/s11228-023-00679-y
Keywords
Surjectivity; Metric regularity; Set-valued map; Implicit mapping theorem; Frechet-montel space; Nash-Moser-Ekeland theory
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This paper presents a new derivative criterion for metric regularity of set-valued maps from a Frechet-Montel space to a Frechet space. Previous studies on such criteria have mainly focused on Banach spaces, but our work extends the research based on the Nash-Moser-Ekeland approach. As a result of our criterion, an implicit mapping result is also provided in this paper.
This paper is devoted to new derivative criterion of metric regularity for set-valued map from a Frechet-Montel space to a Frechet space. Such type of criteria have been well studied in Banach spaces. Our work extends recent studies motivated by Nash-Moser-Ekeland approach. As a consequence of our criterion, an implicit mapping result is also given in the paper.
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