A fixed point theorem of Banach--Caccioppoli type on a class of generalized metric spaces

By A. Branciari. Publicationes mathematicae (Debrecen), 2000

450 citations recorded by the source corpus.

We give a fixed point theorem related to the contraction mapping principle of Banach and Caccioppoli; here we have considered generalized metric spaces, that is metric spaces with the triangular inequality replaced by similar ones which involve four or more points instead of three. At the end of the paper an example is provided to show the improvement of our result with respect to the classical one.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a6eaa6c2a5fd693783060fc7bf43d32b7b4b38dd

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Fixed point results in generalized metric spaces without Hausdorff property (2014, methodology): “The following definition was given by Branciari in [1].”
Generalized Metric Spaces Do Not Have the Compatible Topology (2014, background): “The authors in [12] stated the proof in [1] is incorrect and gave a proof under the assumption that (X, d) is Hausdorff and ] = 2.”
Fixed point of contractive mappings in generalized metric spaces (2009, background): “So instead of following ([1]), it seems more appropriate to rename the convergence as g.”
Common fixed points for α-ψ-φ-contractions in generalized metric spaces (2014, background): “Recently, a very interesting generalization was obtained in [1] by changing the structure of the space itself.”
A FIXED POINT THEOREM IN A GENERALIZED METRIC SPACE FOR MAPPINGS SATISFYING A CONTRACTIVE CONDITION OF INTEGRAL TYPE (2009, unknown): “Then, a Banach-accioppoli contraction also satisfies (1).”
On a new generalization of metric spaces (2018, background): “In [2], Branciari suggested a new generalization of the metric notion by replacing the triangle inequality (iii) by a more general one involving four points.”
Some Unique Fixed Point Theorems in Multiplicative Metric Spaces (2014, background): “Branciari [4] introduced the concept of generalized metric spaces by putting a general inequality condition in place of usual triangular inequality in metric space.”
ON GENERALIZED METRIC SPACES: A SURVEY (2014, methodology): “Using the preceding lemmas, it is easy to show that all the mentioned results from [3, 6, 8, 12, 13, 28, 29] are in fact true as their proofs can be repaired.”
Some Common Fixed Point Results in Rectangular Metric Spaces (2013, background): “(2) In 2000, Branciari [2] introduced the notion of a generalized (rectangular) metric space where the triangle inequality of a metric space was replaced by another inequality, the socalled rectangular inequality.”
Discussion on Contractions on Generalized Metric Spaces (2014, background): “Although the statement is true, in the proof, Branciari [1] used the continuity of generalized metric which cannot be guaranteed.”
THE KANNAN'S FIXED POINT THEOREM IN A CONE RECTANGULAR METRIC SPACE (2009, methodology): “A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ.”
Interpolative Ćirić-Reich-Rus Type Contractions via the Branciari Distance (2019, background): “On the other hand, the concept of a Branciari distance space has been introduced by Brianciari [10] where the triangular inequality is replaced by a quadrilateral one.”
A FIXED POINT THEOREM IN A GENERALIZED METRIC SPACE (2007, background): “We prove a fixed point theorem for uniformly locally contractive mappings in a generalized metric space, a concept recently introduced in [1].”