关于渐近伪压缩映象迭代逼近的表征

摘要

Let C be a nonempty bounded closed convex subset of a Banach space X, and T: C → C be uniformly L-Lipschitzian with L ≥ 1 and asymptotically pseudocontractive with a sequence {kn}(U)[1, ∞), limn→∞ kn = 1. Fix u ∈ C. For each n ≥ 1, xn is a unique fixed point of the contraction Sn(x) = (1 - tn/Lkn)u + tn/Lkn Tnx (A)x ∈ C, where {tn}(U)[0, 1).Under suitable conditions, the strong convergence of the sequence{xn}to a fixed point of T is characterized.%设C是Banach空间X的非空有界闭凸子集,T:C→C既是一致L-Lipschitz映象,L≥1,又是渐近伪压缩映象,具有序列{kn}(U)[1,∞),limn→∞ kn=1.固定u∈C.对每个n≥1,xn是压缩映象Sn(x)=(1-tn/Lkn)u+tn/LknTnx,Ax∈C的唯一不动点,其中,{tn}(U)[0,1).在适当的条件下,本文表征了序列{xn}强收敛到T的不动点.