Abstract
The paper extends the radius of metric regularity theorem by Dontchev, Lewis and Rockafellar (2003) by providing an exact formula for the radius with respect to Lipschitz continuous perturbations in general Asplund spaces, thus, answering affirmatively an open question raised twenty years ago by Ioffe. In the non-Asplund case, we give a natural upper bound for the radius complementing the conventional lower bound in the theorem by Dontchev, Lewis and Rockafellar.
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The authors wish to thank the referees for their unique dedication and hard work reading the manuscript, checking every detail, and making impressive effort to help us improve the text. The paper has indeed strongly benefited from the comments and suggestions of the referees.
Many thanks to the Editor-in-Chief for the perfect choice of the referees and overall handling of our manuscript.
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The second author benefited from the support of the Australian Research Council, project DP160100854, and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska–Curie Grant Agreement No. 823731 CONMECH. Open Access funding enabled and organized by CAUL and its Member Institutions
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Gfrerer, H., Kruger, A.Y. The Radius of Metric Regularity Revisited. Set-Valued Var. Anal 31, 20 (2023). https://doi.org/10.1007/s11228-023-00681-4
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DOI: https://doi.org/10.1007/s11228-023-00681-4