Generalized metrics and Caristi’s theorem

被引:0
作者
William A Kirk
Naseer Shahzad
机构
[1] University of Iowa,Department of Mathematics
[2] King Abdulaziz University,Department of Mathematics
来源
Fixed Point Theory and Applications | / 2013卷
关键词
fixed points; contraction mappings metric spaces; semimetric spaces; generalized metric spaces; Caristi’s theorem;
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摘要
A ‘generalized metric space’ is a semimetric space which does not satisfy the triangle inequality, but which satisfies a weaker assumption called the quadrilateral inequality. After reviewing various related axioms, it is shown that Caristi’s theorem holds in complete generalized metric spaces without further assumptions. This is noteworthy because Banach’s fixed point theorem seems to require more than the quadrilateral inequality, and because standard proofs of Caristi’s theorem require the triangle inequality.
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