Abstract
In this work we present a general theorem concerning chain rules for linear openness of set-valued mappings acting between metric spaces. As particular cases, we obtain classical and also some new results in this field of research, including the celebrated Lyusternik–Graves Theorem. The applications deal with the study of the well-posedness of the solution mappings associated to parametric systems. Sharp estimates for the involved regularity moduli are given.
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Acknowledgments
The authors are indebted to the referees for their valuable comments and suggestions. This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS—UEFISCDI, project number PN-II-ID-PCE-2011-3-0084.
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Durea, M., Strugariu, R. Chain rules for linear openness in metric spaces and applications. Math. Program. 143, 147–176 (2014). https://doi.org/10.1007/s10107-012-0598-8
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DOI: https://doi.org/10.1007/s10107-012-0598-8
Keywords
- Composition of set-valued mappings
- Linear openness
- Metric regularity
- Aubin property
- Implicit multifunctions
- Local composition-stability
- Parametric systems