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A generalized Banach contraction principle that characterizes metric completeness
Proceedings of the American Mathematical Society · 2007 · Vol. 136(5) · pp. 1861–1869
Tomonari Suzuki✉(Kyushu Institute of Technology)
Abstract
We prove a fixed point theorem that is a very simple generalization of the Banach contraction principle and characterizes the metric completeness of the underlying space. We also discuss the Meir-Keeler fixed point theorem.
Fixed Point Theorems AnalysisAdvanced Differential Geometry ResearchContraction principleFixed-point theoremMathematicsMetric spaceCompleteness (order theory)Contraction (grammar)Banach spaceEberlein–Šmulian theoremGeneralizationFixed point
Funding
- Ministry of Education, Culture, Sports, Science and Technology
- Japan Society for the Promotion of Science
Citations
484
FWCI
9.55
field-weighted impact
References
30
Percentile
99%
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Citations per year
References
On the variational principle
Journal of Mathematical Analysis and Applications · 1974 · 2,312 citations
A generalization of Banach’s contraction principle
Proceedings of the American Mathematical Society · 1974 · 808 citations
Fixed point theorems for mappings satisfying inwardness conditions
Transactions of the American Mathematical Society · 1976 · 620 citations
A theorem on contraction mappings
Journal of Mathematical Analysis and Applications · 1969 · 729 citations
A Generalization of Banach's Contraction Principle
Proceedings of the American Mathematical Society · 1974 · 466 citations
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