- Title
- About error bounds in metrizable topological vector spaces
- Creator
- Abbasi, Malek; Théra, Michel
- Date
- 2022
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/192396
- Identifier
- vital:17984
- Identifier
-
https://doi.org/10.1007/s11228-022-00643-2
- Identifier
- ISSN:1877-0533 (ISSN)
- Abstract
- This paper aims to present some sufficient criteria under which a given function between two spaces that are either topological vector spaces whose topologies are generated by metrics or metrizable subsets of some topological vector spaces, satisfies the error bound property. Then, we discuss the Hoffman estimation and obtain some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows to calculate the coefficient of the error bound. The applications of this presentation are illustrated by some examples. © 2022, This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply.
- Publisher
- Springer Science and Business Media B.V.
- Relation
- Set-Valued and Variational Analysis Vol. 30, no. 4 (2022), p. 1291-1311
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © Springer Nature B.V. 2022
- Subject
- 4901 Applied mathematics; 4904 Pure mathematics; Error bound; Hadamard directional derivative; Hoffman estimate; Homogeneously continuous functions; Strongly regular point; Translation invariant metric
- Reviewed
- Funder
- This research benefted from the support of the FMJH Program PGMO and from the support of EDF
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