Random fixed points of increasing compact random maps

Ismat Beg

Archivum Mathematicum (2001)

  • Volume: 037, Issue: 4, page 329-332
  • ISSN: 0044-8753

Abstract

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Let ( Ω , Σ ) 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 : Ω × [ a , b ] → E is an increasing compact random map such that a ≤ f ( ω , a ) and f ( ω , b ) ≤ b for each ω ∈ Ω then f possesses a minimal random fixed point α and a maximal random fixed point β .

How to cite

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Beg, Ismat. "Random fixed points of increasing compact random maps." Archivum Mathematicum 037.4 (2001): 329-332. <http://eudml.org/doc/248757>.

@article{Beg2001,
abstract = {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 $.},
author = {Beg, Ismat},
journal = {Archivum Mathematicum},
keywords = {random fixed point; random map; measurable space; ordered Banach space; random fixed point; random map; measurable space; ordered Banach space},
language = {eng},
number = {4},
pages = {329-332},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Random fixed points of increasing compact random maps},
url = {http://eudml.org/doc/248757},
volume = {037},
year = {2001},
}

TY - JOUR
AU - Beg, Ismat
TI - Random fixed points of increasing compact random maps
JO - Archivum Mathematicum
PY - 2001
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 037
IS - 4
SP - 329
EP - 332
AB - 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 $.
LA - eng
KW - random fixed point; random map; measurable space; ordered Banach space; random fixed point; random map; measurable space; ordered Banach space
UR - http://eudml.org/doc/248757
ER -

References

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