Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections

Authors: Brown A.L.¹; Deutsch F.²; Indumathi V.³; Kenderov P.S.⁴

Source: Journal of Approximation Theory, Volume 115, Number 1, March 2002 , pp. 120-143(24)

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Abstract:

A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection P_M onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dimensional subspace has a continuous C₀(T) and L₁() that have this property are determined. © 2002 Elsevier Science (USA).

Keywords: lower semicontinuity; continuous selection; set valued mapping; approximate lower semicontinuity; weak lower semicontinuity; best approximation; derived mapping; metric projection; geometry of Banach spaces; space of continuous functions; L_p-space

Language: English

Document Type: Research article

Affiliations: 1: D11 IMTECH Colony, Sector 39A, Chandigarh, 160036, India 2: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania, U.S.A., 16802 3: Department of Mathematics, Pondicherry University, Pondicherry, 605 014, India 4: Institute of Mathematics and Informatics, Acad. G. Bonchev-Street, Block 8, Sofia, Bulgaria

Publication date: 2002-03-01