Chapter

Convergence Methods for Double Sequences and Applications

pp 41-61

Almost Regular Matrices

  • M. MursaleenAffiliated withDepartment of Mathematics, Aligarh Muslim University
  • , S. A. MohiuddineAffiliated withDepartment of Mathematics, King Abdulaziz University

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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