Metric Regularity for Set-Valued Maps in Frechet-Montel Spaces. Implicit Mapping Theorem

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.

Automated summary

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.