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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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Banach Contraction Principle: A Centurial Journey
2023Tomar, Anita, Jain, Manish
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Fixed Point Results in b-Metric Spaces Over Banach Algebra and Contraction Principle
Lecture Notes in Mechanical Engineering, 2022Ramakant Bhardwaj
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Some remarks on the generalized Banach contraction principle
Technical Transactions. Fundamental Sciences = Czasopismo Techniczne. Nauki Podstawowe, 2015This paper presents some results concerning the Generalized Banach Contraction Principle proved in 2003 by A. Arvanitakis. In some special cases the constant M can be replaced by a continuous, nonincreasing function 0<=φ(d(x,y))<=1 such that φ(t)=1 if, and only if, t=0.
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A Generalized Banach Contraction Principle That Characterizes Metric Completeness
Proceedings of the American Mathematical Society, 2008Tomonari Suzuki
exaly
Banach Contraction Principle and Ruin Probabilities in Regime-Switching Models
Insurance: Mathematics and Economics, 2018Lesław Gajek, Marcin Rudz
exaly