We discuss the dynamics beyond topological hyperbolicity considering homeomorphisms satisfying shadowing property and generalizations of expansivity. It is proved that transitive countably expansive are in set points. This contrast with pseudo-Anosov diffeomorphisms two-dimensional sphere transitive, cw-expansive, satisfy but dynamical ball each point contains a Cantor subset. exhibit examples ...

In this paper, we introduce two new types of enriched contractions, viz., A-contraction and A-contraction. Then obtain fixed points mappings satisfying such contractions using the point property average operator mappings. Further, study well-posedness limit shadowing problem involving give some examples to validate results proved. Our work improves Berinde P?curar?s recent on different kinds we...