Iterative Methods for Pseudocontractive Mappings in Banach Spaces
Keyword(s):
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.
1976 ◽
Vol 19
(1)
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pp. 7-12
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2002 ◽
Vol 31
(4)
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pp. 251-257
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2005 ◽
Vol 2005
(11)
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pp. 1685-1692
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2018 ◽
Vol 17
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pp. 67-87
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2010 ◽
pp. 181-191
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2011 ◽
Vol 50-51
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pp. 718-722
2020 ◽
Vol 2020
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pp. 1-4