an:05702388 Zbl 1186.47070 Moore, Chika; Nnanwa, C.P.; Ugwu, B.C. Approximation of common random fixed points of finite families of N-uniformly $L_i$-Lipschitzian asymptotically hemicontractive random maps in Banach spaces. EN Banach J. Math. Anal. 3, No. 2, 77-85, electronic only (2009). ISSN 1735-8787/e 2009

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*47J25 47H40 47H06 47H09 N-uniformly $L_i$-Lipschitzian; finite family; asymptotically hemicontractive map; explicit iteration; Banach space 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.