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Regularity Modulus and Radius of Set-Valued Mappings

Abstract

In this paper, we first establish an exact modulus of metrical regularity for set-valued mappings from a complete metric space to a coherent metric space in terms of slopes of the lower semicontinuous envelope of distance functions to the images of set-valued mappings under consideration. Secondly, under suitable assumptions on range spaces and/or on set-valued mappings under consideration, we give an exact estimate for the radius of metric regularity.

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Acknowledgements

This research is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant 101.99-2013.24. The author wishes to thank the anonymous referees and the guest editor for carefully reading the paper and providing valuable comments and suggestions.

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Correspondence to Huynh Van Ngai.

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Dedicated to Professor B. S. Mordukhovich on the occasion of his 65th birthday.

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Van Ngai, H. Regularity Modulus and Radius of Set-Valued Mappings. Vietnam J. Math. 42, 567–578 (2014). https://doi.org/10.1007/s10013-014-0100-4

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  • DOI: https://doi.org/10.1007/s10013-014-0100-4

Keywords

  • Coherency
  • Metrical regularity
  • Openness
  • Slope

Mathematics Subject Classification (2010)

  • 49J52
  • 49J53
  • 90C30