Geodesic
The characteristic of noncompact convexity and random fixed point theorem for set-valued operators
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 269-279 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $(\Omega ,\Sigma )$ be a measurable space, $X$ a Banach space whose characteristic of noncompact convexity is less than 1, $C$ a bounded closed convex subset of $X$, $KC(C)$ the family of all compact convex subsets of $C.$ We prove that a set-valued nonexpansive mapping $T\: C\rightarrow KC(C)$ has a fixed point. Furthermore, if $X$ is separable then we also prove that a set-valued nonexpansive operator $T\: \Omega \times C\rightarrow KC(C)$ has a random fixed point.
Let $(\Omega ,\Sigma )$ be a measurable space, $X$ a Banach space whose characteristic of noncompact convexity is less than 1, $C$ a bounded closed convex subset of $X$, $KC(C)$ the family of all compact convex subsets of $C.$ We prove that a set-valued nonexpansive mapping $T\: C\rightarrow KC(C)$ has a fixed point. Furthermore, if $X$ is separable then we also prove that a set-valued nonexpansive operator $T\: \Omega \times C\rightarrow KC(C)$ has a random fixed point.
Classification : 47H09, 47H10, 47H40
Keywords: random fixed point; set-valued random operator; measure of noncompactness 
@article{CMJ_2007_57_1_a21,
     author = {Kumam, Poom and Plubtieng, Somyot},
     title = {The characteristic of noncompact convexity and random fixed point theorem for set-valued operators},
     journal = {Czechoslovak Mathematical Journal},
     pages = {269--279},
     year = {2007},
     volume = {57},
     number = {1},
     mrnumber = {2309965},
     zbl = {1174.47042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a21/}
}
TY  - JOUR
AU  - Kumam, Poom
AU  - Plubtieng, Somyot
TI  - The characteristic of noncompact convexity and random fixed point theorem for set-valued operators
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 269
EP  - 279
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a21/
LA  - en
ID  - CMJ_2007_57_1_a21
ER  - 
%0 Journal Article
%A Kumam, Poom
%A Plubtieng, Somyot
%T The characteristic of noncompact convexity and random fixed point theorem for set-valued operators
%J Czechoslovak Mathematical Journal
%D 2007
%P 269-279
%V 57
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a21/
%G en
%F CMJ_2007_57_1_a21
Kumam, Poom; Plubtieng, Somyot. The characteristic of noncompact convexity and random fixed point theorem for set-valued operators. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 269-279. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a21/