On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings (Q2577159)

The authors study the weak and strong convergence of the implicit iteration sequences \(\{ x_{n}\} \) defined by: \[ \begin{aligned} x_{n}&= \alpha _{n}x_{n-1} + (1-\alpha _{n})T^{k(n)}_{i(n)}x_{n} + u_{n}, \quad n \geq 1\quad\text{and}\\ x_{n}&=\alpha _{n}x_{n-1} + (1- \alpha _{n})T^{k(n)}_{i(n)}x_{n},\quad n \geq 1\end{aligned} \] to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in real uniformly convex Banach spaces. Their results extend and improve results of several other authors.