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Keywords:
random fixed point; random map; measurable space; ordered Banach space
random fixed point; random map; measurable space; ordered Banach space
Summary:
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 $.
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