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Authors: GABRIELA APREUTESEI, TEODOR PRECUPANU.
Received 18 May 2023; Accepted 27 November 2023. Published Online: 2024-03-20
Published Print: 2024-03-30
pp. 83-92
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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.
