Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces
Morales, Claudio H.
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 625-630 / Harvested from Czech Digital Mathematics Library
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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 $K$.

Publié le : 1992-01-01
Classification:  47H04,  47H09,  47H10 
@article{118534,
     author = {Claudio H. Morales},
     title = {Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {625-630},
     zbl = {0794.47038},
     mrnumber = {1240184},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118534}
}

Morales, Claudio H. Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 625-630. http://gdmltest.u-ga.fr/item/118534/

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