## Banach Journal of Mathematical Analysis

### 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.

#### Article information

Source
Banach J. Math. Anal., Volume 3, Number 2 (2009), 77-85.

Dates
First available in Project Euclid: 17 December 2009

https://projecteuclid.org/euclid.bjma/1261086711

Digital Object Identifier
doi:10.15352/bjma/1261086711

Mathematical Reviews number (MathSciNet)
MR2525109

Zentralblatt MATH identifier
1186.47070

#### Citation

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. Banach J. Math. Anal. 3 (2009), no. 2, 77--85. doi:10.15352/bjma/1261086711. https://projecteuclid.org/euclid.bjma/1261086711