An Introduction to Metric Spaces and Fixed Point Theory

723 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Graph convolutional networks: a comprehensive review (2019, methodology): “f is restricted to a contraction mapping to ensure convergence and suggested by the Banach’s fixed point theorem [67].”
Fixed point and continuation results for contractions in metric and gauge spaces (2007, background): “The reader is referred to [32, 29, 30, 36, 37] and the references therein for more results on contractive and non-expansive mappings.”
On asymptotic pointwise contractions in metric spaces (2009, background): “Keywords: Asymptotic pointwise contraction mapping, asymptotic pointwise nonexpansive mapping, multivalued mappings, fixed point, hyperconvex metric spaces, CAT(0) spaces, uniformly convex metric spaces.”
The random-utility-based multiregional input-output model: solution existence and uniqueness (2004, methodology): “Assuming that the conditions for price solution existence and uniqueness hold, the sequence generated by the iterative function ( 1) ( ) ( ) t t b f b + = v v v converges on the unique solution ( ) b f b = v v v , if ( ) o b b K ∈ v ( Khamsi and Kirk, 2001).”
Graph Neural Networks: A Review of Methods and Applications (2018, methodology): “With the suggestion of Banach’s fixed point theorem (Khamsi and Kirk, 2011), GNN uses the following classic iterative scheme to compute the state:”