Fixed-point theorems for multivalued non-expansive mappings without uniform convexity
Benavides, T. Domínguez ; Ramírez, P. Lorenzo
Abstr. Appl. Anal., Tome 2003 (2003) no. 7, p. 375-386 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Let $X$ be a Banach space whose characteristic of noncompact convexity is less than $1$ and satisfies the nonstrict Opial condition. Let $C$ be a bounded closed convex subset of $X$ , $KC(C)$ the family of all compact convex subsets of $C$ , and $T$ a nonexpansive mapping from $C$ into $KC(C)$ . We prove that $T$ has a fixed point. The nonstrict Opial condition can be removed if, in addition, $T$ is a $1$ - $\chi$ -contractive mapping.
Publié le : 2003-03-26
Classification:  47H04,  47H09,  47H10 
@article{1050425969,
     author = {Benavides, T. Dom\'\i nguez and Ram\'\i rez, P. Lorenzo},
     title = {Fixed-point theorems for multivalued non-expansive mappings without uniform convexity},
     journal = {Abstr. Appl. Anal.},
     volume = {2003},
     number = {7},
     year = {2003},
     pages = { 375-386},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1050425969}
}

Benavides, T. Domínguez; Ramírez, P. Lorenzo. Fixed-point theorems for multivalued non-expansive mappings without uniform convexity. Abstr. Appl. Anal., Tome 2003 (2003) no. 7, pp.  375-386. http://gdmltest.u-ga.fr/item/1050425969/