Pp. 277-314 (38)
In this chapter, the fundamental results on double sequences and related topics
are given. In particular, the concept of convergence of double series in the Pringsheim's
sense is defined, certain spaces of double sequences are introduced, and their
α-,fi β-, duals are determined. Additionally, some classes of four dimensional
matrices are characterized.
Double sequence, convergence of a double sequence in the Pringsheim's
sense, boundedness of a double sequence, regular convergence of a double
sequence, Pringsheim, regular, bounded and absoolute convergence of a doubla series,
Silverman-Toeplitz and Steinhaus theorems for double sequences, convergence
tests for double series, Cauchy product of double series, α-, β-, duals of a space
of double sequences, characterization of some classes of four dimensional matrices.