Results 171 to 180 of about 1,320,516 (202)

Local Generalizations of Banach’s Contraction Mapping Principle

Journal of Analysis, 2022
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Priyam Chakraborty
exaly   +2 more sources

A Generalization of the Banach Contraction Principle

Journal of Mathematical Analysis and Applications, 2002
The authors prove the following nontrivial generalization of the Banach Contraction Principle.
Merryfield, James, Stein, James D. jun.
exaly   +3 more sources

Banach Contraction Principle and Applications

2018
Banach 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-
Praveen Agarwal, Mohamed Jleli, Bessem Samet   +2 more
exaly   +2 more sources

A Simple Proof of the Banach Contraction Principle

Journal of Fixed Point Theory and Applications, 2007
We give a simple proof of the Banach contraction lemma. Mathematics Subject Classification (2000). Primary 55M20.
exaly   +2 more sources

Extensions of Banach's Contraction Principle

Numerical Functional Analysis and Optimization, 2010
Let 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, 2016
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Martínez-Moreno, Juan, Sintunavarat, Wutiphol, Kumam, Poom   +2 more
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The Banach Contraction Principle

2019
In 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

2001
We 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, 2017
In 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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Banach Contraction Principle and Its Generalizations

2013
In 1922, the Polish mathematician Stefan Banach established a remarkable fixed point theorem known as the “Banach Contraction Principle” (BCP) which is one of the most important results of analysis and considered as the main source of metric fixed point theory.
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