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

DOI10.1186/s13663-015-0444-9zbMath1347.54002OpenAlexW1863657822WikidataQ59427802 ScholiaQ59427802MaRDI QIDQ288121

Simeon Reich, Zaslavski, Alexander J.

Publication date: 24 May 2016

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13663-015-0444-9

zbMATH Keywords

fixed pointnonexpansive mappingcomplete metric spaceset-valued mappinghyperbolic spaceBanach spaceporous setBaire categoryinfinite productcontractive mappingapproximate fixed pointbounded linear regularityholomorphic mappingweak ergodic theorem

Mathematics Subject Classification ID

Complete metric spaces (54E50) Baire category, Baire spaces (54E52) Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Research exposition (monographs, survey articles) pertaining to general topology (54-02)

Related Items (2)

On generalized convex contractions of type-2 in b-metric and 2-metric spaces ⋮ On (α,p)-convex contraction and asymptotic regularity

Cites Work

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• Optimization on metric and normed spaces
• Nonconvex optimal control and variational problems
• Porosity and the bounded linear regularity property
• Infinite products of holomorphic mappings
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• Genericity in nonlinear analysis
• A Weak Ergodic Theorem for Infinite Products of Holomorphic Mappings
• A Note on Contractive Mappings
• Nonexpansive iterations in hyperbolic spaces
• On Projection Algorithms for Solving Convex Feasibility Problems
• Generic contractivity for a class of nonlinear mappings

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