Four dimensional matrix characterization P-convergence fields of summability methods
Document Type
Article
Publication Date
2-21-2013
Abstract
In 1945 Agnew presented two dimensional matrix characterization of convergent fields. The goal of this paper is to present four dimensional matrix characterization of P-convergent field. This will be accomplished by the presentation of the following multiple dimensional analogues of Agnew's theorem. If A is a four-dimensional multiplicative with multiplier 0, then there are sequences 0= σ0<σ1<σ2<⋯ and 0=ρ0<ρ1< ρ2<⋯ of integers such that each bounded double sequence {xk,l} oscillating so slowly that P-lim m,nmaxσm≤k,r≤σm+1ρn ≤l,s≤ρn+1x k,l-xr, s=0is A summable to 0 in the Pringsheim sense. In addition, natural implications and variations are also presented.© 2013 Elsevier Inc. All rights reserved.
Publication Title
Applied Mathematics and Computation
Volume
219
Issue
12
First Page
6783
Last Page
6791
Digital Object Identifier (DOI)
10.1016/j.amc.2012.12.069
ISSN
00963003
Citation Information
Patterson. (2013). Four dimensional matrix characterization P-convergence fields of summability methods. Applied Mathematics and Computation, 219(12), 6783–6791. https://doi.org/10.1016/j.amc.2012.12.069