Viscosity Approximate Methods for a Finite Family of Asymptotically Pseudocontractive Mappings
Zhenhua He, Feng Gu · 2009
Let K be a nonempty closed convex and bounded subset of a real Banach space E; Let f: K → K be a contraction map with a con-tractive constant α ∈ (0, 1) and Ti: K → K, i = 1, 2, · · · , N, be N uniformly L-Lipschitzian, asymptotically pseudocontractive maps with sequences {k(i)n}, and uniformly asymptotically regular with sequence {εn}. Suppose {xn} is generated iteratively by xn+1: = λnθnf(xn)+ [1−λn(1+θn)]xn+λnT nn xn n ≥ 1, where Tn = Tn(mod N), x1 ∈ K is a given point. If {λn}, {θn} ⊂ [0, 1] satisfy appropriate conditions, then lim n→ ∞ ‖xn − Tlxn ‖ = 0 for each l ∈ {1, 2, · · · , N}.