  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.
