Recent results on the topological fixed point theory of multivalued mappings: a survey

DOI10.1186/s13663-015-0432-0zbMath1338.54001OpenAlexW1880308494WikidataQ59407558 ScholiaQ59407558MaRDI QIDQ288182

Jan Andres, Lech Gorniewicz

Publication date: 25 May 2016

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

Full work available at URL: https://doi.org/10.1186/s13663-015-0432-0

zbMATH Keywords

fixed pointsdifferential inclusionsmultivalued mappingsfixed point indexLefschetz fixed point theoremabsolute neighborhood retracts and multiretractsejective and repulsive fixed pointsmultivalued fractalsrandom fixed pointsrandom operators

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Fixed-point theorems (47H10) Set-valued operators (47H04) Fixed-point and coincidence theorems (topological aspects) (54H25) Ordinary differential inclusions (34A60) Ordinary differential equations and systems with randomness (34F05) Fractals (28A80) Fixed points and coincidences in algebraic topology (55M20) Absolute neighborhood retracts (55M15) Random nonlinear operators (47H40) Research exposition (monographs, survey articles) pertaining to general topology (54-02) Research exposition (monographs, survey articles) pertaining to algebraic topology (55-02)

Related Items

On the fixed point theory of soft metric spaces ⋮ Note on essential fixed points of approximable multivalued mappings

Cites Work

• Random topological degree and random differential inclusions
• Hyperbolic sets, transversal homoclinic trajectories, and symbolic dynamics for \(C^ 1\)-maps in Banach spaces
• On a generalization of absolute neighborhood retracts
• Another generalization of the Schauder fixed point theorem
• A further generalization of the Schauder fixed point theorem
• Randomized Sharkovsky-type results and random subharmonic solutions of differential inclusions
• On Essential Fixed Points of Compact Mappings on Arbitrary Absolute Neighborhood Retracts and Their Application to Multivalued Fractals
• Topological Analysis
• FIXED POINT THEORY FOR MULTIMAPS IN EXTENSION TYPE SPACES
• Calculation of Lefschetz and Nielsen numbers in hyperspaces for fractals and dynamical systems
• Fixed point theory for compact absorbing contractive admissible type maps
• The Lefschetz fixed point theorem for some noncompact multi-valued maps
• METRIC AND TOPOLOGICAL MULTIVALUED FRACTALS
• RANDOM FIXED POINT THEORY FOR MULTIVALUED COUNTABLY CONDENSING RANDOM OPERATORS
• On the Lefschetz fixed point theorem for Random multivalued mappinngs
• Randomization of Sharkovskii-type theorems
• Topological Fixed Point Theory of Multivalued Mappings
• Note on Nonejective Topological Fractals on Peano's Continua
• Essential and Non Essential Fixed Points
• Essential Sets and Fixed Points
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