Affiliation:
1. Department of Mathematics, Dong-A University, Busan 604-714, Republic of Korea
Abstract
LetEa reflexive Banach space having a uniformly Gâteaux differentiable norm. LetCbe a nonempty closed convex subset ofE,T:C→Ca continuous pseudocontractive mapping withF(T)≠∅, andA:C→Ca continuous bounded strongly pseudocontractive mapping with a pseudocontractive constantk∈(0,1). Let{αn}and{βn}be sequences in(0,1)satisfying suitable conditions and for arbitrary initial valuex0∈C, let the sequence{xn}be generated byxn=αnAxn+βnxn-1+(1-αn-βn)Txn, n≥1.If either every weakly compact convex subset ofEhas the fixed point property for nonexpansive mappings orEis strictly convex, then{xn}converges strongly to a fixed point ofT, which solves a certain variational inequality related toA.
Subject
Applied Mathematics,Analysis
Cited by
1 articles.
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