Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces

Morales, Claudio H.. "Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 33.4 (1992): 625-630. <http://eudml.org/doc/247359>.

@article{Morales1992,
abstract = {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 $r>0$, $\Vert x-y\Vert \le \Vert (1+r)(x-y)-r(u-v)\Vert $. Denote by $G(z,w)$ the set $\lbrace u\in K :\Vert u-w\Vert \le \Vert u-z\Vert \rbrace $. 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 $K$.},
author = {Morales, Claudio H.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {pseudo-contractive mappings; multivalued operator; fixed point property; nonexpansive selfmappings},
language = {eng},
number = {4},
pages = {625-630},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces},
url = {http://eudml.org/doc/247359},
volume = {33},
year = {1992},
}

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
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 4
SP - 625
EP - 630
AB - 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 $r>0$, $\Vert x-y\Vert \le \Vert (1+r)(x-y)-r(u-v)\Vert $. Denote by $G(z,w)$ the set $\lbrace u\in K :\Vert u-w\Vert \le \Vert u-z\Vert \rbrace $. 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 $K$.
LA - eng
KW - pseudo-contractive mappings; multivalued operator; fixed point property; nonexpansive selfmappings
UR - http://eudml.org/doc/247359
ER -