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

Chika Moore, C. P. Nnanwa, and B. C. Ugwu

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1261086711

Digital Object Identifier
doi:10.15352/bjma/1261086711

Mathematical Reviews number (MathSciNet)
MR2525109

Zentralblatt MATH identifier
1186.47070

Subjects
Primary: 47H06: Accretive operators, dissipative operators, etc.
Secondary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47J25: Iterative procedures [See also 65J15]

Keywords
N-uniformly $L_i$-Lipschitzian finite family asymptotically hemicontractive map explicit iteration Banach space

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


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