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Banach Contraction Principle and Applications
2018Banach contraction principle is a fundamental result in Metric Fixed Point Theory. It is a very popular and powerful tool in solving the existence problems in pure and applied sciences. In this chapter, Banach contraction principle and its converse are presented. Moreover, various applications of this famous principle, including mixed Volterra–Fredholm-
P Agarwal +2 more
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A simple proof of the Banach contraction principle
Journal of Fixed Point Theory and Applications, 2007We give a simple proof of the Banach contraction lemma. Mathematics Subject Classification (2000). Primary 55M20.
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The Banach contraction mapping principle and cohomology [PDF]
, 2000 If \(X\) is a metrizable topological space, \(M(X)\) denotes the set of all compatible metrics on \(X\). In the paper it is proved that if \(X\) is compact and \(T:X\to X\) continuous then \(T\) is a Banach contraction relative to some \(d_1\in M(X)\) if and only if there exists some \(d_2\in M(X)\) which is a coboundary of the system \((X\times X, T ...
Janoš, Ludvík
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A Converse of the Banach Contraction Principle for Partial Metric Spaces and the Continuum Hypothesis [PDF]
Results in Mathematics, 2023 A version of the Bessaga inverse of the Banach contraction principle for partial metric spaces is presented. Equivalence of that version and the continuum hypothesis is shown as well.Comment: Corrected formulation of Theorem 5; wording of Theorems 6 and ...
Piotr Mackowiak
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Extensions of Banach's Contraction Principle
Numerical Functional Analysis and Optimization, 2010Let A and B be nonempty subsets of a metric space. As a non-self mapping T: A → B does not necessarily have a fixed point, it is of considerable interest to find an element x that is as close to Tx as possible. In other words, if the fixed point equation Tx = x has no exact solution, then it is contemplated to find an approximate solution x such that ...
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Banach’s Contraction Principle for Nonlinear Contraction Mappings in Modular Metric Spaces
Bulletin of the Malaysian Mathematical Sciences Society, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martínez-Moreno, Juan +2 more
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The Banach Contraction Principle
2019In this case, it is readily seen that there exists the smallest value \(\lambda \) for which the inequality holds, called the Lipschitz constant of f.
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On the Banach Contraction Principle for Multivalued Mappings
2001We give a survey of recent results concerning the Banach contraction principle for multivalued mappings. Nevertheless, this survey contains also some new so far unpublished results. The following main problems are concerned: (i) existence of fixed points (ii) topological structure of the set of fixed points (iii ...
Jan Andres, Lech Górniewicz
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Degree representation of Banach contraction principle in fuzzymetric spaces
Journal of Intelligent & Fuzzy Systems, 2017In this paper, a new approach to Banach contraction principle in fuzzy metric space is provided. The concepts of convergent sequence, Cauchy sequence, complete metric space, contractive map and existence of fixed points, are all defined with some degrees. Adopting these degree concepts, a degree representation of Banach contradiction principle in fuzzy
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