SELECTIVE INERTIAL BLOCK-ITERATIVESCHEMES FOR A CLASS OF VARIATIONALINEQUALITIES AND APPLICATIONS
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Abstract
Our purpose in this paper is to present inertial block-iterative schemes
with selective technique for finding a solution of a variational inequality prob-
lem over the set of common fixed points of a finite family of demiclosed quasi-
nonexpansive mappings in Hilbert spaces. First, we introduce a basic scheme
and show that any sequence, generated by this scheme, converges weakly to a
point in the common fixed point set. Then, based on a specific combination of
the scheme with the steepest-descent method, we propose new schemes, strong
convergence of which is proved without the approximately shrinking and bound-
edly regular assumptions on the mappings and their fixed point sets, respec-
tively, that are usually required recently in literature. An application to study a
networked system and computational experiments are given for illustration and
comparison
with selective technique for finding a solution of a variational inequality prob-
lem over the set of common fixed points of a finite family of demiclosed quasi-
nonexpansive mappings in Hilbert spaces. First, we introduce a basic scheme
and show that any sequence, generated by this scheme, converges weakly to a
point in the common fixed point set. Then, based on a specific combination of
the scheme with the steepest-descent method, we propose new schemes, strong
convergence of which is proved without the approximately shrinking and bound-
edly regular assumptions on the mappings and their fixed point sets, respec-
tively, that are usually required recently in literature. An application to study a
networked system and computational experiments are given for illustration and
comparison
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