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AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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STUDIA MATHEMATICA - Ediţia nr.1 din 2024 | |||||||
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A DUAL MAPPING ASSOCIATED TO A CLOSED CONVEX SET AND SOME SUBDIFFERENTIAL PROPERTIES. Autori: GABRIELA APREUTESEI, TEODOR PRECUPANU. |
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Rezumat: DOI: 10.24193/subbmath.2024.1.06 Received 18 May 2023; Accepted 27 November 2023. Published Online: 2024-03-20 Published Print: 2024-03-30 pp. 83-92 VIEW PDF FULL PDF In this paper we establish some properties of the multivalued mapping (x, d) _ DC (x; d) that associates to every element x of a linear normed space X the set of linear continuous functionals of norm d _ 0 and which separates the closed ball B (x; d) from a closed convex set C _ X. Using this mapping we give links with other important concepts in convex analysis (ε-approximation element, ε-subdifferential of distance function, duality mapping, polar cone). Thus, we establish a dual characterization of ε -approximation elements with respect to a nonvoid closed convex set as a generalization of a known result of Garkavi. Also, we give some properties of univocity and monotonicity of mapping DC: Mathematics Subject Classification (2010): 32A70, 41A65, 46B20, 46N10. Keywords: Distance function associated to a set, ε-subdifferential, best approximation element, ε-monotonicity, separating hyperplane. |
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