Implicit random iteration process with errors for asymptotically quasi-nonexpansive in the intermediate sense random operators (Q2901955)

Let \((\Omega ,\Sigma )\) be a measurable space, \(C\) a closed, convex subset of a separable Banach space, and \(\{ T_1,\dots,T_N\}\) a family of random operators from \(C\) to \(C\), i.e., \(T_i:\Omega \times C\to C\). The author studies the implicit iteration process with errors defined by NEWLINE\[NEWLINE\xi _n(\omega )=\alpha _n\xi _{n-1}(\omega )+\beta _nT_{i(n)}^{k(n)} (\omega ,\xi _n(\omega ))+\gamma _nf_n(\omega ),NEWLINE\]NEWLINE where \(n=(k(n)-1)N+i(n)\), \(i(n)\in\{ 1,2,\dots,N\}\), \(f_n:\Omega \to C\) and \(\alpha _n+\beta _n+\gamma _n=1\) for \(n\geq 1\). He gives rather complicated sufficient conditions for the convergence of the sequence \(\{ \xi _n\}\) to a common random fixed point of \(T_1,\dots,T_N\).NEWLINENEWLINE Reviewer's remark: It is not clear if the sequence \(\{\xi _n\}\) is well defined.