Matrix transformations of classes of geometric sequences

For any fixed t satisfying 0 < t < 1, let Gt denote the set of all sequences which are dominated by a constant multiple of any sequence [rⁿ] with r < t. In this paper we characterize three kinds of matrix transformations: (i) those from Gt to the convergent sequences, (ii) those from G_t to the null sequences, and (iii) those from G_t to the bounded sequences. Also, the classes of three well-known summability methods are investigated as mappings on G_t.