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Erschienen in:
Open Access 01.12.2006 | Research Article
An approximation method for continuous pseudocontractive mappings
Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006
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Abstract
Let
be a closed convex subset of a real Banach space
,
is continuous pseudocontractive mapping, and
is a fixed
-Lipschitzian strongly pseudocontractive mapping. For any
, let
be the unique fixed point of
. We prove that if
has a fixed point and
has uniformly Gâteaux differentiable norm, such that every nonempty closed bounded convex subset of
has the fixed point property for nonexpansive self-mappings, then
converges to a fixed point of
as
approaches to 0. The results presented extend and improve the corresponding results of Morales and Jung (2000) and Hong-Kun Xu (2004).
be a closed convex subset of a real Banach space
,
is continuous pseudocontractive mapping, and
is a fixed
-Lipschitzian strongly pseudocontractive mapping. For any
, let
be the unique fixed point of
. We prove that if
has a fixed point and
has uniformly Gâteaux differentiable norm, such that every nonempty closed bounded convex subset of
has the fixed point property for nonexpansive self-mappings, then
converges to a fixed point of
as
approaches to 0. The results presented extend and improve the corresponding results of Morales and Jung (2000) and Hong-Kun Xu (2004).