Almost Convergence of Double Sequences

M. Mursaleen and S. A. Mohiuddine
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M. Mursaleen: Aligarh Muslim University, Department of Mathematics
S. A. Mohiuddine: King Abdulaziz University, Department of Mathematics

Chapter Chapter 2 in Convergence Methods for Double Sequences and Applications, 2014, pp 17-39 from Springer

Abstract: Abstract The notion of almost convergence for ordinary (single) sequences was given by Lorentz (Acta Math. 80:167–190, 1948), and for double sequences by Moricz and Rhoades (Math. Proc. Camb. Philos. Soc. 104:283–294, 1988). In this chapter, we discuss the notion of almost convergence and almost Cauchy for double sequences. Some more related spaces for double sequences, associated sublinear functionals, and various inclusion relations are also studied.

Keywords: Double sequences; Convergence in Pringsheim’s sense; Boundedly convergence; Regular convergence; Almost convergence; (C; 1; 1)-convergence; Banach limits for double sequences; Strongly almost convergence; Almost Cauchy; Strongly Cesàro summable double sequences; Sublinear functionals; Abel’s transformation for double series (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1611-7_2

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DOI: 10.1007/978-81-322-1611-7_2

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