Genericity and porosity in fixed point theory: a survey of recent results

We survey recent results regarding genericity and porosity in fixed point theory. These results concern, inter alia , infinite products, nonexpansive mappings, approximate fixed points, contractive mappings, bounded linear regularity, set-valued mappings, holomorphic mappings and weak ergodic theore...

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Vydané v:Fixed point theory and applications (Hindawi Publishing Corporation) Ročník 2015; číslo 1; s. 1 - 21
Hlavní autori: Reich, Simeon, Zaslavski, Alexander J
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 29.10.2015
Predmet:
Analysis
Applications of Mathematics
Approximation
Differential Geometry
Ergodic processes
Fixed points (mathematics)
Mapping
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Metric space
Porosity
Regularity
Review
Theorems
Topology
bounded linear regularity
54E52
complete metric space
54E50
46T25
contractive mapping
nonexpansive mapping
hyperbolic space
Banach space
porous set
54H25
47H10
Baire category
fixed point
weak ergodic theorem
37C20
46G20
approximate fixed point
infinite product
47H09
set-valued mapping
holomorphic mapping
ISSN:1687-1812, 1687-1812
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Popis
Shrnutí:We survey recent results regarding genericity and porosity in fixed point theory. These results concern, inter alia , infinite products, nonexpansive mappings, approximate fixed points, contractive mappings, bounded linear regularity, set-valued mappings, holomorphic mappings and weak ergodic theorems. We consider both normed linear spaces and hyperbolic metric spaces.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1687-1812
1687-1812
DOI:10.1186/s13663-015-0444-9