<p>This paper, in the setting <i>at infinity</i>, presents some relationships between the modulus of metric regularity and the radius of (strong) metric regularity that gives a measure of the extent to which a set-valued mapping can be perturbed before (strong) metric regularity is lost. The results given here can be viewed as versions at infinity of [<CitationRef CitationID="CR2">2</CitationRef>, Theorem&#xa0;1.5] and [<CitationRef CitationID="CR3">3</CitationRef>, Theorem&#xa0;4.6].</p>

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The radius of metric regularity at infinity

  • MINH TÙNG NGUYẼXN,
  • TIẼN SO’N PHẠM

摘要

This paper, in the setting at infinity, presents some relationships between the modulus of metric regularity and the radius of (strong) metric regularity that gives a measure of the extent to which a set-valued mapping can be perturbed before (strong) metric regularity is lost. The results given here can be viewed as versions at infinity of [2, Theorem 1.5] and [3, Theorem 4.6].