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Characterizations of Some Transversality-Type Properties

Abstract

Primal characterizations (necessary and sufficient conditions) and slope characterizations of subtransversality, intrinsic transversality and transversality are obtained. The metric nature of intrinsic transversality is established. The relation of intrinsic transversality and tangential transversality is clarified. The equivalence of our characterization of intrinsic transversality and the primal characterization of intrinsic transversality of Thao et al. in the setting of Hilbert spaces is proved, while in general Banach spaces our characterization is less restrictive.

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Acknowledgements

The authors are grateful to Prof. A. Dontchev for his useful comments and suggestions and to the unknown referees for their careful reading of the manuscript and for the useful remarks that helped to improve it.

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Correspondence to Stoyan Apostolov.

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This work was supported by the Bulgarian National Scientific Fund under Grant KP-06-H22/4/04.12.2018 and by the Sofia University “St. Kliment Ohridski” fund “Research & Development” under contract 80-10-40 /22.03.2021.

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Apostolov, S., Bivas, M. & Ribarska, N. Characterizations of Some Transversality-Type Properties. Set-Valued Var. Anal (2022). https://doi.org/10.1007/s11228-022-00633-4

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  • DOI: https://doi.org/10.1007/s11228-022-00633-4

Keywords

  • (Sub)transversality
  • (Sub)regularity
  • Intrinsic transversality
  • Tangential transversality
  • Primal space characterizations
  • Function slopes

Mathematics Subject Classification (2010)

  • 49J53
  • 46N10
  • 90C30