A new iteration process for approximation of common fixed points for finite families of total asymptotically nonexpansive mappings (Q963516)

Summary: Let \(E\) be a real Banach space and \(K\) a closed convex nonempty subset of \(E\). Let \(T_1,T_2,\dots,T_m:K\to K\) be \(m\) total asymptotically nonexpansive mappings. A simple iterative sequence \(\{x_n\}_{n\geq1}\) is constructed in \(E\) and necessary and sufficient conditions for this sequence to converge to a common fixed point of \(\{Ti\}_{i=1}^m\) are given. Furthermore, in the case that \(E\) is a uniformly convex real Banach space, strong convergence of the sequence \(\{x_n\}_{n=1}^\infty\) to a common fixed point of the family \(\{Ti\}_{i=1}^mA\) is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem.