Stability relative to a set and to the whole space revisited
type: Item
instance of: scholarly article
title: Stability relative to a set and to the whole space revisited
zbMATH Open document ID: 0666.34057
DOI: 10.1016/0096-3003(87)90062-2
author: Khader H. Ahmad
published in: Applied Mathematics and Computation
publication date: 1987-01-01T00:00:00Z
review text: In [Proc. Int. Conf. Nonlinear Oscillations, Kiev 1969, 448-457 (1970; Zbl 0233.34063)] \textit{P. Seibert} suggested without proof some theorems on stability. These theorems involved two new concepts: The first is a local stability of a subset Y of a metric space X on a subset Z of Y. The second is a notion of conditionally attracting set \(Y\subseteq X\) on \(Z\subseteq Y\). Using the first of Seibert's concepts, we suggest new theorems and provide the corresponding proofs. However, our theorems are logically independent of those of Seibert. In addition, a proof of a criterion on local stability suggested by Seibert is given.
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 4089972
zbMATH Keywords: local stability
zbMATH Keywords: conditionally attracting set
MaRDI profile type: Publication
full work available at URL: 0096-3003(87)90062-2
OpenAlex ID: W2012710875
cites work: Q5641468
cites work: Q5614853
description: scientific article; zbMATH DE number 4089972