Convergence theorems of the sequence of iterates for a finite family asymptotically nonexpansive mappings
Jui‐Chi Huang · International Journal of Mathematics and Mathematical Sciences · 2001
Let E be a uniformly convex Banach space, C a nonempty closed convex subset of E . In this paper, we introduce an iteration scheme with errors in the sense of Xu (1998) generated by as follows: , j = 1, 2, …, r , x 1 ∈ C , , n ≥ 1, where U n (0) : = I , I the identity map; and { u n ( j ) } are bounded sequences in C ; and { a n ( j ) }, { b n ( j ) }, and { c n ( j ) } are suitable sequences in [0, 1]. We first consider the behaviour of iteration scheme above for a finite family of asymptotically nonexpansive mappings. Then we generalize theorems of Schu and Rhoades.