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Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities
Journal of Inequalities and Applications volume 2008, Article number: 284345 (2007)
Abstract
Let be a real
-uniformly smooth Banach space with constant
,
. Let
and
be a nonexpansive map and an
-strongly accretive map which is also
-Lipschitzian, respectively. Let
be a real sequence in
that satisfies the following condition:
and
. For
and
, define a sequence
iteratively in
by
,
,
. Then,
converges strongly to the unique solution
of the variational inequality problem
(search for
such that
for all
, where
. A convergence theorem related to finite family of nonexpansive maps is also proved.
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Chidume, C.E., Chidume, C.O. & Ali, B. Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities. J Inequal Appl 2008, 284345 (2007). https://doi.org/10.1155/2008/284345
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DOI: https://doi.org/10.1155/2008/284345