Applications of the proximity map to fixed point theorems in Hilbert space

Tzu Chu Lin; Chi Lin Yen

doi:10.1016/0021-9045(88)90053-6

Applications of the proximity map to fixed point theorems in Hilbert space

Tzu Chu Lin^*
, Chi Lin Yen

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

Abstract

We extend Lin's result (Canad. Math. Bull. 22, No. 4 (1979), 513-515) and Singh and Watsons' result (J. Approx. Theory 39 (1983), 72-76) to more general 1-set-contractive maps. This class of 1-set-contractive maps includes condensing (or densifying) maps and nonexpansive maps; it also includes other important maps such as semicontractive maps and LANE maps. As applications of our theorems, fixed point theorems are proved under various conditions. The main idea we use, is one due to Cheney and Goldstein (Proc. Amer. Math. Soc. 10 (1959), 448-450), that a proximity map in Hilbert space is nonexpansive.

Original language	English
Pages (from-to)	141-148
Number of pages	8
Journal	Journal of Approximation Theory
Volume	52
Issue number	2
DOIs	https://doi.org/10.1016/0021-9045(88)90053-6
Publication status	Published - 1988 Feb

ASJC Scopus subject areas

Analysis
Numerical Analysis
General Mathematics
Applied Mathematics

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AB - We extend Lin's result (Canad. Math. Bull. 22, No. 4 (1979), 513-515) and Singh and Watsons' result (J. Approx. Theory 39 (1983), 72-76) to more general 1-set-contractive maps. This class of 1-set-contractive maps includes condensing (or densifying) maps and nonexpansive maps; it also includes other important maps such as semicontractive maps and LANE maps. As applications of our theorems, fixed point theorems are proved under various conditions. The main idea we use, is one due to Cheney and Goldstein (Proc. Amer. Math. Soc. 10 (1959), 448-450), that a proximity map in Hilbert space is nonexpansive.

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Applications of the proximity map to fixed point theorems in Hilbert space

Abstract

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