Matrix Transforms into the Subsets of Maddox Spaces Defined by Speed

Let λ and μ be monotonically increasing strictly positive sequences, i.e., the speeds of convergence. Earlier the notions of boundedness, convergence, and zero-convergence with the speed are known. In this paper, the notions of paranormed boundedness, convergence, and zero-convergence with speed have been defined. The matrix transforms from the sets of bounded, convergent, and zero-convergent sequences with the speed λ into the sets of paranormed bounded, paranormed convergent, and paranormed zero-convergent sequences with the speed μ are studied.