Geodesic
Random fixed points of increasing compact random maps
Archivum mathematicum, Tome 37 (2001) no. 4, pp. 329-332 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $(\Omega ,\Sigma )$ be a measurable space, $(E,P)$ be an ordered separable Banach space and let $[a,b]$ be a nonempty order interval in $E$. It is shown that if $f:\Omega \times [a,b]\rightarrow E$ is an increasing compact random map such that $a\le f(\omega ,a)$ and $f(\omega ,b)\le b$ for each $\omega \in \Omega $ then $f$ possesses a minimal random fixed point $\alpha $ and a maximal random fixed point $\beta $.
Let $(\Omega ,\Sigma )$ be a measurable space, $(E,P)$ be an ordered separable Banach space and let $[a,b]$ be a nonempty order interval in $E$. It is shown that if $f:\Omega \times [a,b]\rightarrow E$ is an increasing compact random map such that $a\le f(\omega ,a)$ and $f(\omega ,b)\le b$ for each $\omega \in \Omega $ then $f$ possesses a minimal random fixed point $\alpha $ and a maximal random fixed point $\beta $.
Classification : 47H10, 47H40, 60H25
Keywords: random fixed point; random map; measurable space; ordered Banach space 
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     author = {Beg, Ismat},
     title = {Random fixed points of increasing compact random maps},
     journal = {Archivum mathematicum},
     pages = {329--332},
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     mrnumber = {1879455},
     zbl = {1068.47079},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2001_37_4_a8/}
}
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Beg, Ismat. Random fixed points of increasing compact random maps. Archivum mathematicum, Tome 37 (2001) no. 4, pp. 329-332. http://geodesic.mathdoc.fr/item/ARM_2001_37_4_a8/

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