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Random fixed point equations and inverse problems using “collage method” for contraction mappings. (English) Zbl 1121.47048

The paper is concerned with direct and inverse problems for the random fixed point equations \(T(\omega,x(\omega))=x(\omega)\), where \(T: \Omega \times X \to X\) is a given operator, \(\Omega\) is a probability space and \(X\) is a Polish metric space. Applications to random integral equations and to random iterated function systems are considered.

MSC:

47H40 Random nonlinear operators
47H10 Fixed-point theorems
60H25 Random operators and equations (aspects of stochastic analysis)
65J22 Numerical solution to inverse problems in abstract spaces
47N30 Applications of operator theory in probability theory and statistics
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