Four dimensional matrix mappings and applications

Abstract

In this paper, we characterize the classes (L, L-k) , (L-k, L) and (L-8, L-k) , 1 = k < 8, of all four dimen-sional infinite matrices, where L-k and L-8 are the spaces of all absolutely k-summable and bounded dou-ble sequences, respectively. Using them, we establish some relations between |N/, p(n), q(n)| and |N/, p'(n), q'(n)|(k)summability methods which extend some results of Bosanquet (1950), Sarigol (1993), Sarigol & Bor (1995), and Sunouchi (1949) to double summability methods, and give a relation between single and double summability methods.