No abstract

Abstract. Two results are given, which use Tabor groupoids for questions of stability in the sense of Pólya-Szegő-Hyers-Ulam. We also start to study Tabor groupoids in their own right. Mathematics Subject Classification (2010). 20N02, 39B82.Keywords. Tabor groupoids, stability of functional equations, bounded perturbations of additive functions.

We characterize the closure of the set of iterable functions in the space of all continuous self-mappings of a real compact interval endowed with the supremum norm. A full description of iterable functions was given by M. C. Zdun. , almost iterable functions, approximately iterable functions, closure of the set of the iterable functions.

Abstract. In this paper we consider stability in the Ulam-Hyers sense, and in other similar senses, for the five equivalent definitions of one-dimensional dynamical systems.Mathematics Subject Classification. Primary 39B12, 39B82; Secondary 37E05, 26A18.