Approximation of common random fixed points of finite families of N-uniformly $L_i$-Lipschitzian asymptotically hemicontractive Random maps in Banach spaces

Abstract

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 $T : \Omega \times K \to K$, such that $\{T_i\}_{i=1}^N$, be N-uniformly $L_i$-Lipschitzian asymptotically hemicontractive random maps of $K$ with $F=\displaystyle\bigcap_{i=1}^N F(T_i)\ne \emptyset$. We construct an explicit iteration scheme and prove neccessary and sufficient conditions for approximating common fixed points of finite family of asymptotically hemicontractive random maps.