Bi-asymptotic c-expansivity

In this paper, we define bi-asymptotically c-expansive maps on metric spaces and study its relationship with other variants of expansivity such as bi-asymptotically expansive maps and N-expansive maps. We also provide an example to establish that expansive homeomorphisms need not be bi-asymptotically expansive. Finally, we prove a spectral decomposition theorem for bi-asymptotically c-expansive continuous surjective maps with the shadowing property on compact metric spaces.(c) 2023 Elsevier Inc. All rights reserved.