Stability relative to a set and to the whole space revisited
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.
scientific article; zbMATH DE number 4089972