Generalized Virtually Stable Maps and Their Associated Sequences

Abstract

We extend the concept of virtual stability of continuous self-maps to arbitrary selfmaps and investigate the structure of sequences associated with uniformly virtually stable selfmaps. We also obtain a necessary and sufficient condition for a uniformly virtually stable selfmap to have the largest possible associated sequence. Examples of a uniformly virtually stable selfmap having the prescribed largest sequence and a uniformly virtually stable selfmap having no largest sequence are given.

Strict stability of fixed points and iteration schemes

“…Proposition 2.47. [6] Let (X, d) be a metric sapce. Then f is virtually nonexpansive if and only if f is uniformly virtually stable with respect to (n).…”