Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 4, pp. 625-630
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Let $X$ be a real Banach space. A multivalued operator $T$ from $K$ into $2^X$ is said to be pseudo-contractive if for every $x,y$ in $K$, $u\in T(x)$, $v\in T(y)$ and all $r>0$, $\|x-y\|\leq \|(1+r)(x-y)-r(u-v)\|$. Denote by $G(z,w)$ the set $\{u\in K :\|u-w\|\leq \|u-z\|\}$. Suppose every bounded closed and convex subset of $X$ has the fixed point property with respect to nonexpansive selfmappings. Now if $T$ is a Lipschitzian and pseudo-contractive mapping from $K$ into the family of closed and bounded subsets of $K$ so that the set $G(z,w)$ is bounded for some $z\in K$ and some $w\in T(z)$, then $T$ has a fixed point in $K$.
@article{CMUC_1992__33_4_a7,
author = {Morales, Claudio H.},
title = {Multivalued pseudo-contractive mappings defined on unbounded sets in {Banach} spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {625--630},
publisher = {mathdoc},
volume = {33},
number = {4},
year = {1992},
mrnumber = {1240184},
zbl = {0794.47038},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_1992__33_4_a7/}
}
TY - JOUR AU - Morales, Claudio H. TI - Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces JO - Commentationes Mathematicae Universitatis Carolinae PY - 1992 SP - 625 EP - 630 VL - 33 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CMUC_1992__33_4_a7/ LA - en ID - CMUC_1992__33_4_a7 ER -
%0 Journal Article %A Morales, Claudio H. %T Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces %J Commentationes Mathematicae Universitatis Carolinae %D 1992 %P 625-630 %V 33 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/CMUC_1992__33_4_a7/ %G en %F CMUC_1992__33_4_a7
Morales, Claudio H. Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 4, pp. 625-630. http://geodesic.mathdoc.fr/item/CMUC_1992__33_4_a7/