Some Classes of Matrix Transformations between the Subsets of Maddox Spaces Defined by Speed

Let X, Y be two sets of sequences with real or complex entries, and (X, Y) the set of all matrices with real or complex entries to map X into Y. Let λ and μ be speeds of convergence, i.e., monotonically increasing strictly positive sequences. In this paper, some classes of matrix transforms, where X is the subset of certain Maddox space defined by λ, and Y is the subset of another Maddox space defined by μ, have been characterized. The application possibilities of the main results are demonstrated with two examples.