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

Tzu Chu Lin*, Chi Lin Yen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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 languageEnglish
Pages (from-to)141-148
Number of pages8
JournalJournal of Approximation Theory
Issue number2
Publication statusPublished - 1988 Feb

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • General Mathematics
  • Applied Mathematics


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