Abstract: In this paper, we introduced the notions of q-equicontinuous points and q-sensitive points. We showed that a point x ∈ X is mean equicontinuous point of a dynamical system (X, T) if and only if it is a q-equicontinuous point of (X, T) for any q belongs to[0,1). And a point x ∈ X is mean sensitive point of a dynamical system (X, T) if and only if it is a q-sensitive (X, T) point for some q belongs to (0, 1].

Key words: Equicontinuous, Sensitive, Mean equicontinuous, Mean sensitive