Random fixed point theorems and approximation

DOI10.1080/07362999708809466zbMath0892.47060OpenAlexW2028144066MaRDI QIDQ3128360

George Xian-Zhi Yuan, Kok-Keong Tan

Publication date: 13 August 1998

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362999708809466

zbMATH Keywords

random fixed pointmeasurable selectiondemiclosedrandom approximationproximity maprandom nonexpansive operators\(k\)-set-contractioncondensing densifying operatorhemi-compact maprandom 1-set-contractionrandom continuous condensing mappingsrandom demicompact map

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Fixed-point theorems (47H10) Set-valued operators (47H04) Fixed-point and coincidence theorems (topological aspects) (54H25) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Best approximation, Chebyshev systems (41A50) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Random operators and equations (aspects of stochastic analysis) (60H25) Random nonlinear operators (47H40)

Related Items (14)

Deterministic and random coincidence point results for \(f\)-nonexpansive maps ⋮ Approximation of *-nonexpansive random multivalued operators on Banach spaces ⋮ A general framework for spatial GARCH models ⋮ Random fixed point theorems for nonself mappings ⋮ Random fixed point theorem of Krasnoselskii type for the sum of two operators ⋮ Random fixed point theorems for 1-set-contractive multivalued random maps ⋮ On Random Approximations and Random Fixed Point Theorems for 1‐Set‐Contractive Random Maps ⋮ Equivalence and stability of random fixed point iterative procedures ⋮ Random and deterministic fixed point and approximation results for countably 1-set-contractive multimaps ⋮ Random Coincidence Point Theorem in Fréchet Spaces with Applications ⋮ Random fixed points of 1-set contractive random maps in Fréchet spaces ⋮ A random coincidence point theorem ⋮ Approximation of random fixed points in normed spaces ⋮ Random fixed points for several classes of 1-ball-contractive and 1-set-contractive random maps

Cites Work

• Extensions of two fixed point theorems of Ky Fan
• Some properties of convex sets related to fixed point theorems
• Proximity maps and fixed points
• Applications of the proximity map to fixed point theorems in Hilbert space
• Random integral equations
• On fixed point theorems obtained from existence theorems for differential equations
• Approximate selections, best approximations, fixed points, and invariant sets
• Random fixed point theorems with an application to random differential equations in Banach spaces
• Random fixed-point theorems and approximation in cones
• Random fixed points and viable random solutions of functional- differential inclusions
• Extensions of two fixed point theorems of F. E. Browder
• Fixed point theorems for set-valued maps in infinite dimensional spaces
• The fixed point index for local condensing maps
• Some random fixed point theorems
• Fixed point theorems in probabilistic analysis
• On a sharpened form of the Schauder fixed-point theorem
• Semicontractive and semiaccretive nonlinear mappings in Banach spaces
• Weak convergence of the sequence of successive approximations for nonexpansive mappings

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