Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces

Let be a reflexive Banach space having a weakly sequentially continuous duality mapping with gauge function , a nonempty closed convex subset of , and a multivalued nonself-mapping such that is nonexpansive, where . Let be a contraction with constant . Suppose that, for each and , the contrac...

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Bibliographic Details
Main Author: Jong Soo Jung
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/369412
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Summary:Let be a reflexive Banach space having a weakly sequentially continuous duality mapping with gauge function , a nonempty closed convex subset of , and a multivalued nonself-mapping such that is nonexpansive, where . Let be a contraction with constant . Suppose that, for each and , the contraction defined by has a fixed point . Let , and be three sequences in satisfying approximate conditions. Then, for arbitrary , the sequence generated by for all converges strongly to a fixed point of .
ISSN:1085-3375
1687-0409