Open AccessMatrix summability of statistically p-convergence sequences
Author(s) -
Richard F. Patterson,
Ekrem Savaş
Publication year - 2011
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1104055p
Subject(s) - mathematics , sequence (biology) , sequence space , matrix (chemical analysis) , transformation matrix , space (punctuation) , convergence (economics) , pure mathematics , section (typography) , limit of a sequence , combinatorics , mathematical analysis , banach space , physics , linguistics , philosophy , genetics , materials science , kinematics , business , classical mechanics , limit (mathematics) , advertising , economics , composite material , biology , economic growth
Matrix summability is arguable the most important tool used to characterize sequence spaces. In 1993 Kolk presented such a characterization for statistically convergent sequence space using nonnegative regular matrix. The goal of this paper is extended Kolk's results to double sequence spaces via four dimensional matrix transformation. To accomplish this goal we begin by presenting the following multidimensional analog of Kolk's Theorem : Let X be a section-closed double sequence space containing e '' and Y an arbitrary se, quence space. Then B is an element of (st(A)(2) boolean AND X, Y) if and only if B is an element of (c '' boolean AND X, Y) and B-[KxK] is an element of (X, Y) (delta(A) (K x K) = 0). In addition, to this result we shall also present implication and variation of this theorem