Global convergence of successive approximations of solutions for functional differential equations with infinite delay
type: Item
instance of: scholarly article
title: Global convergence of successive approximations of solutions for functional differential equations with infinite delay
zbMATH Open document ID: 0651.34064
author: Jong Son Shin
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1987-01-01T00:00:00Z
review text: The author consideres the initial value problem for functional differential equations with infinite delay (IP): \(dx/dt=f(t,x_ t),\) \(t\geq \sigma\), \(x_{\sigma}=\phi \in B\), where f is an E-valued mapping defined on \(J\times B\), E is a Banach space with norm \(| \cdot |_ E\), \(J=[\sigma,\sigma +a)\), \(0<a\leq \infty\), B is an abstract phase space with seminorm, or quasinorm \(| \cdot |_ B\) satisfying suitable axioms. In four theorems he proves sufficient conditions for the global convergence of successive approximations for (IP). On the end, the obtained results in this paper are illustrated in two examples.
reviewed by: Pavol Marušiak
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 4061719
zbMATH Keywords: global convergence of successive approximations
zbMATH Keywords: examples
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4061719