Communications of the
Korean Mathematical Society CKMS

In the present work we construct a composite implicit random iterative process with errors for a finite family of asymptotically nonexpansive random operators and discuss a necessary and sufficient condition for the convergence of this process in an arbitrary real Banach space. It is also proved that this process converges to the common random fixed point of the finite family of asymptotically nonexpansive random operators in the setting of uniformly convex Banach spaces. The present work also generalizes a recently established result in Banach spaces.

Keywords: composite implicit random iterative process with errors, asymptotically nonexpansive random operators, Condition$(B)$, Banach spaces, measurable spaces

MSC numbers: 47H10