Abstract and Applied Analysis
Volume 2010 (2010), Article ID 582475, 11 pages
doi:10.1155/2010/582475
Research Article

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

Yasunori Kimura

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan

Received 27 August 2010; Accepted 18 December 2010

Academic Editor: Mitsuharu Ôtani

Copyright © 2010 Yasunori Kimura. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.