Abstract and Applied Analysis

Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball

Yasunori Kimura

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Abstract

We propose a new concept of set convergence in a Hadamard space and obtain its equivalent condition by using the notion of metric projections. Applying this result, we also prove a convergence theorem for an iterative scheme by the shrinking projection method in a real Hilbert ball.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 582475, 11 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313170940

Digital Object Identifier
doi:10.1155/2010/582475

Mathematical Reviews number (MathSciNet)
MR2754196

Zentralblatt MATH identifier
1206.54049

Citation

Kimura, Yasunori. Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball. Abstr. Appl. Anal. 2010 (2010), Article ID 582475, 11 pages. doi:10.1155/2010/582475. https://projecteuclid.org/euclid.aaa/1313170940


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