The Banach fixed point theorem: selected topics from its hundred-year history
DOI10.1007/S13398-024-01636-6MaRDI QIDQ6577508
Jacek Jachymski, Izabela Jóźwik, Małgorzata Terepeta
Publication date: 24 July 2024
Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)
contractioncomplete metric spaceBanach spaceBanach fixed point theoremsemimetric spaceapplications of the contraction principle
History of mathematics in the 20th century (01A60) Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) History of mathematics in the 21st century (01A61)
Cites Work
- Another Proof of the Contraction Mapping Principle
- On Nonlinear Contractions
- Square roots in Banach *-algebras
- On Contractive Mappings
- Zur Theorie und Anwendung des Iterationsverfahrens
- Convex analysis and monotone operator theory in Hilbert spaces
- Über Abbildung von Mannigfaltigkeiten.
- Doktorat i doktoranci Stefana Banacha
- Banach's doctorate: a case of mistaken identity
- Title not available (Why is that?)
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- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- On fixed points of locally and pointwise contracting maps
- Metric fixed point theory: a brief retrospective
- Théorie des opérations linéaires.
- On cone metric spaces: a survey
- Banach's fixed point theorem, Ćirić's and Kannan's are equivalent via redefining the metric
- The establishment of functional analysis
- A fixed point theorem and its application to the central limit theorem
- Meir-Keeler contractions of integral type are still Meir-Keeler contractions
- A simple proof of the Banach contraction principle
- Some problems in metric fixed point theory
- Monotone (nonlinear) operators in Hilbert space
- Fuzzy mappings and fixed point theorem
- The contraction principle as a particular case of Kleene's fixed point theorem
- An improved criterion for fixed points of contraction mappings
- Completeness and fixed-points
- A topological characterization of Banach contractions
- A connection between fixed-point theorems and tiling problems
- \(K\)-metric and \(K\)-normed linear spaces: Survey
- Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales.
- A short proof of the converse to the contraction principle and some related results
- A fixed point theorem for mappings satisfying a general contractive condition of integral type
- Elementary fixed point theorems
- Banach contraction principle and ruin probabilities in regime-switching models
- Various extensions of Kannan's fixed point theorem
- Un teorema generale sull' esistenza di elementi uniti in una trasformazione funzionale.
- A generalization of the Banach contraction principle
- Fixed points of asymptotic contractions
- Multi-valued contraction mappings
- Common fixed points for commuting contraction mappings
- A theorem on contraction mappings
- Eine Anwendung des Edelsteinschen Fixpunktsatzes auf Integralgleichungen vom Abel-Liouvilleschen Typ
- Handbook of metric fixed point theory
- An application of Ramsey's Theorem to the Banach Contraction Principle
- Nonlinear Contractions on Semimetric Spaces
- A contraction principle in semimetric spaces
- Fixed Point Theory in Distance Spaces
- On the converse of Banach "fixed-point principle"
- An Extension of Banach's Contraction Principle
- A Note on Contractive Mappings
- On a converse to Banach’s Fixed Point Theorem
- Two Results on Jachymski–Schröder–Stein Contractions
- Shorter Notes: A Short Proof of the Algebraic Weierstrass Preparation Theorem
- An Elementary Proof of the Cauchy-Kowalevsky Theorem
- On Fixed and Periodic Points Under Contractive Mappings
- Remarks on a paper by F. Browder about contraction
- Equivalent Cauchy sequences and contractive fixed points in metric spaces
- A Generalization of Banach's Contraction Principle
- Fixed Point Theorems for Mappings Satisfying Inwardness Conditions
- Positive definite functions and coincidences
- Contractions and completely continuous mappings
- A Comparison of Various Definitions of Contractive Mappings
- Local Contractions in Metric Spaces
- A proof of the Generalized Banach Contraction Conjecture
- A fixed point theorem in partially ordered sets and some applications to matrix equations
- Fixed Point Theorems for Maps With Local and Pointwise Contraction Properties
- An Introduction to Nonlinear Analysis and Fixed Point Theory
- Uniformly Contractive Fixed Points in Compact Metric Spaces
- Completeness and the Contraction Principle
- Integral equations, implicit functions, and fixed points
- Some Thoughts on Polish Contributions to Fixed Point Theory
- Basic Monotonicity Methods with Some Applications
- FIXED-POINT THEOREMS FOR NONCOMPACT MAPPINGS IN HILBERT SPACE
- Zum Prinzip der kontraktiven Abbildung
- Some Theorems on Contractive Mappings
- Fixed Point Theorems and Applications
- The contraction principle for mappings on a metric space with a graph
- A generalized Banach contraction principle that characterizes metric completeness
- A Fixed Point Theorem for Mappings which do not Increase Distances
- Generalizations of the Converse of the Contraction Mapping Principle
- On a Fixed-Point Theorem for Metric Spaces
- A Converse of Banach's Contraction Theorem
- A converse to Banach's contraction theorem
- Properties of Fixed Point Spaces
- A Remark on a Fixed-Point Theorem for Iterated Mappings
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