Open AccessStatistically convergent double sequences
Author(s) -
Binod Chandra Tripathy
Publication year - 2003
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.34.2003.314
Subject(s) - mathematics , sequence (biology) , bounded function , separable space , limit of a sequence , cauchy distribution , convergent series , decomposition theorem , pure mathematics , space (punctuation) , relation (database) , combinatorics , discrete mathematics , mathematical analysis , limit (mathematics) , power series , linguistics , philosophy , genetics , biology , database , computer science
In this aricle we introduce the notion of density of subsets of $ N imes N $. Using this concept we introduce the notion of statistically convergent double sequences and statistically Cauchy double sequences. The decomposition theorem is proved. The inclusion relations are obtained. We have shown that the bounded statistically convergent in Pringsheim's sense sequence space is not separable. A relation between strongly $ p $-Cesaro summability of double sequences and bounded statistically convergent double sequences is established