A generalized Banach contraction principle that characterizes metric completeness

By Tomonari Suzuki. 2007

566 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0b4dcd88398a824868f85d6e044b1751bc872133

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In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications (2011, background): “1 Introduction and preliminaries In 2008 Suzuki [1] introduced a new type of mappings which generalize the wellknown Banach contraction principle [2].”
Fractional-order delayed predator–prey systems with Holling type-II functional response (2015, background): “By Banach contraction principle [42], we can deduce that L has a unique fixed point which implies that our problem has a unique solution.”
Various Suzuki type theorems in b -metric spaces (2015, result): “In 2009, Suzuki [27] proved certain remarkable results to improve the results of Banach and Edelstein (see also [24, 26]).”
SUZUKI-WARDOWSKI TYPE FIXED POINT THEOREMS FOR $\alpha$-GF-CONTRACTIONS (2014, background): “This result has been extended in many directions (see [1-18]).”
Fixed Point Theory in -Complete Metric Spaces with Applications (2014, background): “From Theorem 12 we deduce the following Suzuki type fixed point result.”
On Suzuki-Wardowski type fixed point theorems (2015, unknown): “As an application of our results proved above, we deduce certain Suzuki- Wardowski type …xed point theorems.”
Some fixed point results on a metric space with a graph (2012, methodology): “Suzuki established some methods which extend the well-known contraction methods for mappings and multifunctions (see [15,16]).”
Ćirić type generalized F-contractions on complete metric spaces and fixed point results (2014, background): “Because of its importance for mathematical theory, Banach Contraction Principle has been extended and generalized in many directions (see[1–3, 6, 7, 9–14, 16]).”