Four dimensional matrix mappings and applications

DOI: 10.48129/kjs.17649

Abstract

In this paper, we characterize the classes (L,Lk), (Lk,L) and (L∞,Lk), 1 ≤ k < ∞, of all four dimentional infinite matrices, where Lk and L∞ are the spaces of all absolutely k-summable and bounded double sequences, respectively. Using them, we establish some relations between

N, pn, qn

and

N, p0
n
, q0
n


k
summability methods which extend some results of Bosanquet (Bosanquet 1950), Sarıgol (Sarıg ¨ ol 1993), ¨
Sarıgol and Bor (Sarıg ¨ ol and Bor 1995), and Sunouchi (Sunouchi 1949) to double summability methods, ¨
and give a relation between single and double summability methods.