Almost convergence and a core theorem for double sequences

By Mursaleen, O. H. Edely. 2004

126 citations recorded by the source corpus.

Abstract The idea of almost convergence was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283–294] and they also characterized the four dimensional strong regular matrices. In this paper we define the M-core for double sequences and determine those four dimensional matrices which transform every bounded double sequence x=[xjk] into one whose core is a subset of the M-core of x.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ab618da218ce7477fd2ece39c7b3e188a2490778

Citations in the corpus

• Generalized statistical convergence and statistical core of double sequences (2010, unknown): “…B(qr) = {b(qr)jk : j, k = 1, 2, 3, . . .}, B(q) = {b(q)jk }, C(r) = {c(r)jk } and C = {cjk} as follows: For all j, k, q, r, we set b (qr) jk = ⎧ ⎨ ⎩ 1, if (j, k) = (q, r), 0, otherwise; b (q) jk = ⎧ ⎨ ⎩ 1, if j = q, 0, otherwise; c (r) jk = ⎧ ⎨ ⎩ 1, if k = r, 0, otherwise; and cjk = 1 for all j, k.”
• The semi normed space defined by a double gai sequence of modulus function (2010, unknown): “Nextly, Mursaleen [26] and Mursaleen and Edely [27] have defined the almost strong regularity of matrices for double sequences and applied these matrices to establish a core theorem and introduced the M−core for double sequences and determined those four dimensional matrices transforming every bound”