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On Some Converses of Generalized Banach Contraction Principles
1986The purpose of this paper is to state some converses to generalized contraction principles for pairs of selfmappings on metric spaces.
B. Palczewski, A. Miczko
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Banach Contraction Principle and Its Generalizations
2013In 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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The Banach contraction mapping principle and cohomology
2000If \(X\) 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 ...
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Contraction-Mapping Principles in Scales of Banach Spaces
1989In chapter 3 we have explained a general method for solving initial value problems in abstract scales of Banach spaces. This abstract version of the Cauchy-Kovalevskaya theorem is advantageous because it comprises not only the case of initial value problems for differential equations (cf.
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Banach Contraction Principle its Generalizations and Applications
Advances in Nonlinear Variational InequalitiesThe Banach Contraction Principle (BCP), a cornerstone of fixed-point theory, employs the method of successive approximations to determine fixed points of operator equations. These fixed points often represent solutions to complex mathematical problems, making the principle highly valuable in a wide range of scientific and technological disciplines ...
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