A Generalisation of Contraction Principle in Metric Spaces

By P. Dutta, Binayak S. Choudhury. 2008

502 citations recorded by the source corpus.

Here we introduce a generalisation of the Banach contraction mapping principle. We show that the result extends two existing generalisations of the same principle. We support our result by an example.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4a71f7316c70667736a3718bab7f5b85da907bb8

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In Geometry and Topology

Citations in the corpus

SOME RESULTS ON WEAKLY CONTRACTIVE MAPS (2012, unknown): “[11] Let (X, d) be a complete metric space and let f : X → X be a self-mapping satisfying the inequality ψ(d(fx, fy)) ≤ ψ(d(x, y))− φ(d(x, y)), for some ψ ∈ Ψ and φ ∈ Φ and all x, y ∈ X.”
Some fixed point results for (α,β)-(ψ,Φ)-contractive mappings (2014, background): “Moreover, the result of Dutta and Choudhury [12] can not be applied to f .”
Generalized Metric Spaces Do Not Have the Compatible Topology (2014, unknown): “See also [15].”
Various generalizations of metric spaces and fixed point theorems (2015, background): “proved that several fixed point generalizations to partial metric spaces can be obtained from the corresponding results in metric spaces, such as: [17, Theorem 1] from [32, Theorem 2], [7, Theorem 6] from the main result of [60], [6, Theorem5] from [13, Theorem1.”
Coupled coincidence point theorems in ordered metric spaces (2011, methodology): “In particular, weak contraction principle has been generalized by use of Altering distance functions in [19].”
Some Coincidence Point Theorems for Nonlinear Contraction in Ordered Metric Spaces (2011, background): “Introduction and Preliminaries Generalization of the Banach principle [1] has been heavily investigated by many authors (see [2-14]).”