Convergence Theorems of the Sequence of Iterates for a Finite Family Asymptotically Nonexpansive Mappings
نویسنده
چکیده
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 {Tj : C → C}j=1 as follows: Un(j) = an(j)I+bn(j)T j Un(j−1)+cn(j)un(j), j = 1,2, . . . ,r , x1 ∈ C , xn+1 = an(r)xn+bn(r)T r Un(r−1)xn+cn(r)un(r), n≥ 1, where Un(0) := I, I the identity map; and {un(j)} are bounded sequences in C ; and {an(j)}, {bn(j)}, and {cn(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. 2000 Mathematics Subject Classification. 47H10.
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