Results 171 to 180 of about 1,267,876 (189)

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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Contraction-Mapping Principles in Scales of Banach Spaces

1989
In 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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A Complete Century of Banach Contraction Principle

2023
Tomar, Anita, Jain, Manish, Kumar, Sanjay   +2 more
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On the Correlation between Banach Contraction Principle and Caristi’s Fixed Point Theorem in b-Metric Spaces

Mathematics, 2022
Salvador Romaguera
exaly  

Banach Contraction Principle its Generalizations and Applications

Advances in Nonlinear Variational Inequalities
The 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

2023
Tomar, 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, 2022
Ramakant Bhardwaj
exaly  

Some remarks on the generalized Banach contraction principle

Technical Transactions. Fundamental Sciences = Czasopismo Techniczne. Nauki Podstawowe, 2015
This 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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q-scale function, Banach contraction principle, and ultimate ruin probability in a Markov-modulated jump–diffusion risk model

Scandinavian Actuarial Journal, 2023
exaly  

Some new extensions of Banach’s contraction principle to partial metric space

Applied Mathematics Letters, 2011
Vladimir Rakocevic, Vladimir Pavlovic, Dejan Ilić   +2 more
exaly