Description

• Title:
  Minimal displacement of random variables under Lipschitz random maps
• Creator:
  Beg, Ismag
• Description:
  Let $(\Omega ,\Sigma )$ be a measurable space and $X$ be a separable metric space. It is shown that for measurable maps $\zeta ,\eta \colon \Omega \rightarrow X$, if a random map $T\colon\Omega \times X\rightarrow X$ satisfies $d(T(\omega ,\zeta (\omega )),T(\omega ,\eta (\omega )))\leq \alpha d(\zeta (\omega ),\eta (\omega ))+\gamma $ then $\inf\{d(\xi (\omega ),T(\omega ,\xi (\omega )))\}\leq \gamma/ (1-\alpha)$, where $\gamma > 0$, $\alpha \in (0,1)$ and $\inf$ is taken over all measurable maps $\xi \colon \Omega \rightarrow X$. Several consequences of this result are also obtained.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2002.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 19, No 2 (June 2002); 391 - 397;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.020/9655
• Subject:
  Minimal displacement;
  random contraction;
  nonexpansive random map;
  measurable space;
  metric space;
  47H40;
  47H10;
  47H09;
  60H25;
  54H25
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.020
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other