Analogues of some fundamental theorems of summability theory. (1st January 2000)

• Record Type: Journal Article
• Authors: Patterson, Richard F.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 23:Number 1(2000)
• Page Start: 1
• Page End: 9
• Publication Date: 2000-01-01
• Subjects: Subsequences of a double sequence -- Pringsheim limit point -- P-convergent -- P-divergent -- RH-regular; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171200001782
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : In 1911, Steinhaus presented the following theorem: ifA is a regular matrix then there exists a sequence of 0's and 1's which is notA -summable. In 1943, R. C. Buck characterized convergent sequences as follows: a sequencex is convergent if and only if there exists a regular matrixA which sums every subsequence ofx . In this paper, definitions for “subsequences of a double sequence” and “Pringsheim limit points” of a double sequence are introduced. In addition, multidimensional analogues of Steinhaus' and Buck's theorems are proved.