Abstract and Applied Analysis

Characterizations of metric projections in Banach spaces and applications

Jean-Paul Penot and Robert Ratsimahalo

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Abstract

This paper is devoted to the study of the metric projection onto a nonempty closed convex subset of a general Banach space. Thanks to a systematic use of semi-inner products and duality mappings, characterizations of the metric projection are given. Applications to decompositions of Banach spaces along convex cones and variational inequalities are presented.

Article information

Source
Abstr. Appl. Anal., Volume 3, Number 1-2 (1998), 85-103.

Dates
First available in Project Euclid: 8 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049832682

Digital Object Identifier
doi:10.1155/S1085337598000451

Mathematical Reviews number (MathSciNet)
MR1700278

Zentralblatt MATH identifier
1030.90136

Subjects
Primary: 90C48: Programming in abstract spaces

Keywords
Metric projection closed convex subset of a Banach space semi-inner products duality mappings convex cones

Citation

Penot, Jean-Paul; Ratsimahalo, Robert. Characterizations of metric projections in Banach spaces and applications. Abstr. Appl. Anal. 3 (1998), no. 1-2, 85--103. doi:10.1155/S1085337598000451. https://projecteuclid.org/euclid.aaa/1049832682


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