Almost strongly regular matrices and a core theorem for double sequences

By Mursaleen. 2004

137 citations recorded by the source corpus.

Abstract The idea of almost convergence for double sequences 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 and characterize the almost strongly regular matrices for double sequences and apply these matrices to establish a core theorem.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a5228c2967087858c76b45fcc73f26164b56ffe6

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”