Iterative Methods for Pseudocontractive Mappings in Banach Spaces
Let E a reflexive Banach space having a uniformly Gâteaux differentiable norm. Let C be a nonempty closed convex subset of E, T:C→C a continuous pseudocontractive mapping with F(T)≠∅, and A:C→C a continuous bounded strongly pseudocontractive mapping with a pseudocontractive constant k∈(0,1). Let {αn...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/643602 |
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| Summary: | Let E a reflexive Banach space having a uniformly Gâteaux differentiable norm. Let C be a nonempty closed convex subset of E, T:C→C a continuous pseudocontractive mapping with F(T)≠∅, and A:C→C a continuous bounded strongly pseudocontractive mapping with a pseudocontractive constant k∈(0,1). Let {αn} and {βn} be sequences in (0,1) satisfying suitable conditions and for arbitrary initial value x0∈C, let the sequence {xn} be generated by xn=αnAxn+βnxn-1+(1-αn-βn)Txn, n≥1. If either every weakly compact convex subset of E has the fixed point property for nonexpansive mappings or E is strictly convex, then {xn} converges strongly to a fixed point of T, which solves a certain variational inequality related to A. |
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| ISSN: | 1085-3375 1687-0409 |