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Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
Fixed Point Theory and Applications volume 2008, Article number: 167535 (2008)
Abstract
Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of
has the fixed point property for nonexpansive mappings. Let
be a nonempty closed convex subset of
,
a contractive mapping (or a weakly contractive mapping), and
nonexpansive mapping with the fixed point set
. Let
be generated by a new composite iterative scheme:
,
,
. It is proved that
converges strongly to a point in
, which is a solution of certain variational inequality provided that the sequence
satisfies
and
,
for some
and the sequence
is asymptotically regular.
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Jung, J.S. Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces. Fixed Point Theory Appl 2008, 167535 (2008). https://doi.org/10.1155/2008/167535
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DOI: https://doi.org/10.1155/2008/167535