Direct proofs of intrinsic properties of prox-regular sets in Hilbert spaces

• Autorzy: Konstantinov Matey , Zlateva Nadia

Identyfikatory

DOI

10.1515/jaa-2022-1010

• Języki publikacji: EN

Abstrakty

EN

We provide new proofs of two intrinsic properties of prox-regular sets in Hilbert spaces.

Słowa kluczowe

EN

uniformly prox-regular set; proximally smooth set; distance function; metric projection mapping; Hilbert space

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 1
• Strony: 143--149
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Konstantinov Matey

• Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria

autor

Zlateva Nadia

• Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria

• https://orcid.org/0000-0002-6223-9055

Bibliografia

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• [3] S. Adly, F. Nacry and L. Thibault, Prox-regular sets and Legendre-Fenchel transform related to separation properties, Optimization 71 (2022), no. 7, 2097-2129.
• [4] M. V. Balashov and G. E. Ivanov, Weakly convex and proximally smooth sets in Banach spaces, Izv. Ross. Akad. Nauk Ser. Mat. 73 (2009), no. 3, 23-66; translation in Izv. Math. 73 (2009), no. 3, 455-499.
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• [13] R. A. Poliquin and R. T. Rockafellar, Prox-regular functions in variational analysis, Trans. Amer. Math. Soc. 348 (1996), no. 5, 1805-1838.
• [14] R. A. Poliquin, R. T. Rockafellar and L. Thibault, Local differentiability of distance functions, Trans. Amer. Math. Soc. 352 (2000), no. 11, 5231-5249.
• [15] R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, Grundlehren Math. Wiss. 317, Springer, Berlin, 1998.
• [16] L. Thibault, Unilateral Variational Analysis in Banach Spaces. Part I: General Theory. Part II: Special Classes of Functions and Sets, to appear.
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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).