Existence and uniqueness theorem for a solution of fuzzy Volterra integral equations
type: Item
instance of: scholarly article
title: Existence and uniqueness theorem for a solution of fuzzy Volterra integral equations
zbMATH Open document ID: 0934.45001
DOI: 10.1016/S0165-0114(97)00238-8
author: Jong Yeoul Park
author: Hyo Keun Han
published in: Fuzzy Sets and Systems
publication date: 2000-04-11T00:00:00Z
review text: The authors prove the existence and uniqueness of a solution to the integral equation \[ x(t) = f(t) + \int_{t_0}^t k(t,s,x(s)) ds ,\quad t\in [t_0,t_0+a], \] where the equation is fuzzy in the sense that the values of \(x\) (and \(f\) and \(k\) too) are membership functions on \(R^n\). It is assumed that the functions \(f\) and \((s,t)\mapsto k(t,s,x)\) are levelwise continuous and \(k\) is assumed to be locally Lipschitz-levelwise-continuous in its third variable. The proof uses the method of successive approximations and most of the fuzzy notions that are used are explained.
reviewed by: Gustaf Gripenberg
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 26E50
zbMATH DE Number: 1339646
zbMATH Keywords: fuzzy Volterra integral equation
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
cites work: Integrals of set-valued functions
cites work: Fuzzy differential equations
cites work: The Cauchy problem for fuzzy differential equations
cites work: Q4091811
cites work: Existence of solutions of fuzzy integral equations in Banach spaces
cites work: Common fixed points of fuzzy mappings
cites work: Fuzzy random variables
full work available at URL: s0165-0114(97)00238-8
OpenAlex ID: W2069083443
description: scientific article; zbMATH DE number 1339646