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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