1Department of Applied Mathematics Pukyong National University Pusan 608-737, South Korea 2Department of Mathematics The University of Iowa Iowa City, IA 52242-1419, U.S.A.
Annales Polonici Mathematici, Tome 76 (2001) no. 3, pp. 189-196
Let $X$ be a Banach space, $C$ a closed subset of $X$, and
$T:C\rightarrow C$ a nonexpansive mapping. It has recently been
shown that if $X$ is reflexive and locally uniformly convex and
if the fixed point set $F(T)$ of $T$ has nonempty interior then
the Picard iterates of the mapping $T$ always converge to a
point of $F(T)$. In this paper it is shown that if $T$ is
assumed to be asymptotically regular, this condition can be
weakened much further. Finally, some observations are made about
the geometric conditions imposed.
Keywords:
banach space closed subset rightarrow nonexpansive mapping has recently shown reflexive locally uniformly convex fixed point set has nonempty interior picard iterates mapping always converge point paper shown assumed asymptotically regular condition weakened much further finally observations made about geometric conditions imposed
Affiliations des auteurs :
Eun Suk Kim
1
;
W. A. Kirk
2
1
Department of Applied Mathematics Pukyong National University Pusan 608-737, South Korea
2
Department of Mathematics The University of Iowa Iowa City, IA 52242-1419, U.S.A.
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title = {A note on {Picard} iterates of nonexpansive mappings},
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Eun Suk Kim; W. A. Kirk. A note on Picard iterates of nonexpansive mappings. Annales Polonici Mathematici, Tome 76 (2001) no. 3, pp. 189-196. doi: 10.4064/ap76-3-2
