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An Implicit Hierarchical Fixed-Point Approach to General Variational Inequalities in Hilbert Spaces
Fixed Point Theory and Applications volume 2011, Article number: 748918 (2011)
Abstract
Let be a nonempty closed convex subset of a real Hilbert space
. Let
be a
-Lipschitzian and
-strongly monotone operator with constants
,
be nonexpansive mappings with
where
denotes the fixed-point set of
, and
be a
-contraction with coefficient
. Let
and
, where
. For each
, let
be a unique solution of the fixed-point equation
. We derive the following conclusions on the behavior of the net
along the curve
: (i) if
, as
, then
strongly, which is the unique solution of the variational inequality of finding
such that
and (ii) if
, as
, then
strongly, which is the unique solution of some hierarchical variational inequality problem.
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Zeng, L., Wen, CF. & Yao, J. An Implicit Hierarchical Fixed-Point Approach to General Variational Inequalities in Hilbert Spaces. Fixed Point Theory Appl 2011, 748918 (2011). https://doi.org/10.1155/2011/748918
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DOI: https://doi.org/10.1155/2011/748918