Matrix summability of classes of geometric sequences

Recently Fricke and Fridy [2] introduced the set G of complex number sequences that are dominated by a convergent geometric sequence. In this paper we define a set G_t, for any fixed t satisfying 0 < t < 1, as the set of all the sequences which are dominated by a constant multiple of any sequence {sⁿ} with s < t. We study the matrices which map the set G_t into another similar set G_w as well as mapping into the set G. The characterizations of such matrices are established in terms of their rows and columns. Also, several classes of well-known summability methods are investigated as mappings on G_t or into G_t.