Abstract and Applied Analysis

The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces

Zihou Zhang and Chunyan Liu

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Abstract

We show a necessary and sufficient condition for the existence of metric projection on a class of half-space K x 0 * , c = { x X : x * ( x ) c } in Banach space. Two representations of metric projections P K x 0 * , c and P K x 0 , c are given, respectively, where K x 0 , c stands for dual half-space of K x 0 * , c in dual space X * . By these representations, a series of continuity results of the metric projections P K x 0 * , c and P K x 0 , c are given. We also provide the characterization that a metric projection is a linear bounded operator.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 908676, 5 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273166

Digital Object Identifier
doi:10.1155/2014/908676

Mathematical Reviews number (MathSciNet)
MR3173296

Zentralblatt MATH identifier
07023289

Citation

Zhang, Zihou; Liu, Chunyan. The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces. Abstr. Appl. Anal. 2014 (2014), Article ID 908676, 5 pages. doi:10.1155/2014/908676. https://projecteuclid.org/euclid.aaa/1412273166


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