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Convergence theorems for fixed points of demicontinuous pseudocontractive mappings
Fixed Point Theory and Applications volume 2005, Article number: 475373 (2005)
Abstract
Let be an open subset of a real uniformly smooth Banach space
. Suppose
is a demicontinuous pseudocontractive mapping satisfying an appropriate condition, where
denotes the closure of
. Then, it is proved that (i)
for every
; (ii) for a given
, there exists a unique path
,
, satisfying
. Moreover, if
or there exists
such that the set
is bounded, then it is proved that, as
, the path
converges strongly to a fixed point of
. Furthermore, explicit iteration procedures with bounded error terms are proved to converge strongly to a fixed point of
.
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Chidume, C., Zegeye, H. Convergence theorems for fixed points of demicontinuous pseudocontractive mappings. Fixed Point Theory Appl 2005, 475373 (2005). https://doi.org/10.1155/FPTA.2005.67
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DOI: https://doi.org/10.1155/FPTA.2005.67