Almost and Statistical Convergence of Ordinary Sequences: A Preview

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 1 in Convergence Methods for Double Sequences and Applications, 2014, pp 1-15 from Springer

Abstract: Abstract In this chapter, we recall the notion of almost convergence and statistical convergence for single sequences x=(x k ). We present here a brief survey on developments of almost convergence, statistical convergence, and some related methods, e.g., absolute almost convergence and strong almost convergence for single sequences.

Keywords: Sequence spaces; Schauder basis; FK and BK spaces; Banach limit; Almost convergence; Almost periodic sequences; $\mathcal{A}$ -invariant mean; $\mathcal{A}$ -almost convergence; F A -summable sequences; Absolute and strong almost convergence; Statistical convergence; Statistical limit points and statistical cluster points; Statistical limit superior and statistical limit inferior; Knopp core and statistical core; Matrix transformations (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_1

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DOI: 10.1007/978-81-322-1611-7_1

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