Applications of the proximity map to fixed point theorems in Hilbert space
type: Item
instance of: scholarly article
title: Applications of the proximity map to fixed point theorems in Hilbert space
zbMATH Open document ID: 0643.47053
DOI: 10.1016/0021-9045(88)90053-6
author: Tzu-Chu Lin
author: Chi-Lin Yen
published in: Journal of Approximation Theory
publication date: 1988-01-01T00:00:00Z
review text: The authors prove that if S is a closed convex subset of a Hilbert space X and f is a l-set-contractive map of S into X, satisfying some closure conditions involving the metric projection of X into S, then there exists a point \(u\in S\) such that \(\| u-f(u)\| =d(f(u),S)\). This result is then applied to prove various fixed point theorems, extending results obtained by Ky Fan, F. Browder, W. Petryshyn, S. Reich and the first author. The basic idea used in the proofs is that the metric projection of a Hilbert space into a closed convex subset is nonexpansive.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 4048465
zbMATH Keywords: l-set-contractive map
zbMATH Keywords: metric projection
zbMATH Keywords: fixed point theorems
zbMATH Keywords: closed convex subset
reviewed by: Stefan Cobzaş
MaRDI profile type: Publication
full work available at URL: 0021-9045(88)90053-6
OpenAlex ID: W2066341299
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description: scientific article; zbMATH DE number 4048465