Explicit iteration method for common fixed points of a finite family of nonself asymptotically nonexpansive mappings

摘要

Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E, which is also a nonexpansive retract of E with nonexpansive retraction P. Let {{T_i : i ∈ I} be N nonself asymptotically nonexpansive mappings from K to E such that F = {x ∈ K : T_ix = x,i ∈ I} ≠ φ, where I = {1, 2,..., N}. From arbitrary x_0 ∈ K, {x_n} is defined by x_n = P((1 - α_n)x_(n-1)+α_nT_n(PT_n)~(m-1)x_(n-1)), n ≥ 1 where n = (m - 1)N + i, T_n = T_n(mod N) = T_i, i ∈ I, the mod N function takes values in I, {α_n} is a real sequence in [δ, 1-δ] for some δ ∈ (0, 1). Some strong and weak convergence theorems of {x_n} to some q ∈ F are obtained under some suitable conditions in real uniformly convex Banach spaces.