Approximating Fixed Points of Non-self Nonexpansive Mapping
Xiaolong Qin · Acta Analysis Functionalis Applicata · 2011
Let E be a uniformly convex Banach space and K a nonempty convex closed subsetwhich is also a nonexpansive retract of E.Let T:K→E be a nonexpansive mapping withF(T):= {x∈K:Tx = x}≠Φ.Let α_n,β_n,γ_n,α_n',β_n',γ_n' be real sequences in[0,1]such thatα_n +β_n +γ_n =α_n'+β_n'+γ_n'= 1,starting from arbitrary x_1∈K,define the sequence {x_n} bywith the restrictionsγ_n∞,γ_n'∞.Then(i) If the dual E~* of E has the Kadec-Klee property,then weak convergence of a {x_n} to somex~*∈F(T) is proved;(ii) If T satisfies condition(A),then strong convergence of {x_n} to some x~*∈F(T) is obtained.