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Approximation of common random fixed points of finite families of N-uniformly $L_i$-Lipschitzian asymptotically hemicontractive random maps in Banach spaces. (English) Zbl 1186.47070
Summary: Let $(\Omega,\Sigma,\mu)$ be a complete probability measure space, $E$ be a real separable Banach space, $K$ a nonempty closed convex subset of $E$. Let $T : \Omega \times K \rightarrow K$, such that $\{T_i\}_{i=1}^N$ be $N$-uniformly $L_i$-Lipschitzian asymptotically hemicontractive random maps of $K$ with $F = \cap_{i=1}^N F (T_i) \ne\emptyset$. We construct an explicit iteration scheme and prove necessary and sufficient conditions for approximating common fixed points of a finite family of asymptotically hemicontractive random maps.

47J25Iterative procedures (nonlinear operator equations)
47H40Random operators (nonlinear)
47H06Accretive operators, dissipative operators, etc. (nonlinear)
47H09Mappings defined by “shrinking” properties
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