Almost Regular Matrices

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 3 in Convergence Methods for Double Sequences and Applications, 2014, pp 41-61 from Springer

Abstract: Abstract The Silverman–Toeplitz theorem is a well-known theorem that states necessary and sufficient conditions to transform a convergent sequence into a convergent sequence leaving the limit invariant. This idea was extended to RH-regular matrices by using the notion of P-convergence (see Hamilton in Duke Math. J. 2:29–60, 1936 and Robinson in Trans. Am. Math. Soc. 28:50–73, 1926). In this chapter, we use the notion of almost convergence to define and characterize almost conservative, almost regular, strongly regular, and almost strongly regular four-dimensional matrices.

Keywords: Four-dimensional infinite matrices; $\mathcal{C}_{\nu }$ -conservative and $\mathcal{C}_{\nu }$ -regular matrices; Bounded-regular matrices; Almost $\mathcal{C}_{\nu }$ -conservative and almost $\mathcal{C}_{\nu }$ -regular matrices; Strongly regular matrices; Almost strongly regular (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-81-322-1611-7_3

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