Random-valued functions and iterative functional equations
type: Item
instance of: scholarly article
title: Random-valued functions and iterative functional equations
zbMATH Open document ID: 1060.39017
author: Witold Jarczyk
author: Karol Baron
published in: Aequationes Mathematicae
publication date: 2004-11-26T00:00:00Z
review text: Given a random-valued function \(f: [0,1] \times \Omega \to [0,1]\) on a probability space \((\Omega, A, P)\), the authors consider the bounded solutions \(\psi : [0,1] \to R\) of the inequality \[ \psi (x) \leq \int_{\Omega} \psi (f(x, \omega)) \,dP (\omega) \] A uniqueness type problem for bounded solutions \(\varphi\) of equations of the type \[ \varphi (x) = h ( x , \varphi \circ f(x, \cdot)) \] is studied. Results for \( f: R \times \Omega \to R\) of the form \( f( x, \omega) = z + \xi (\omega)\) are proved. Some particular cases are studied in more details, especially those where the probability space under considerations is simply the set of positive integers.
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 39B62
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 2119231
zbMATH Keywords: iterative equations
zbMATH Keywords: real-valued function
zbMATH Keywords: bounded continuous solutions
zbMATH Keywords: functional inequality
zbMATH Keywords: probability space
MaRDI profile type: Publication
full work available at URL: s00010-003-2717-3
OpenAlex ID: W1968610050
DOI: 10.1007/S00010-003-2717-3
description: scientific article; zbMATH DE number 2119231