Summability Theory And Its Applications

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The theory of summability has many uses throughout analysis and applied mathematics. Engineers and physicists working with Fourier series or analytic continuation will also find the concepts of ...
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Double Sequences

Pp. 277-314 (38)

Feyzi Basar

Abstract

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.

Keywords:

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.