TY - JOUR
T1 - Matrix transformations and Walsh's equiconvergence theorem
AU - Selvaraj, Chikkanna R.
AU - Selvaraj, Suguna
PY - 2005/10/3
Y1 - 2005/10/3
N2 - In 1977, Jacob defines Gα, for any 0 ≤ α < ∞, as the set of all complex sequences x such that lim sup xk 1/k ≤ α. In this paper, we apply Gu - Gv matrix transformation on the sequences of operators given in the famous Walsh's equiconvergence theorem, where we have that the difference of two sequences of operators converges to zero in a disk. We show that the Gu - Gv matrix transformation of the difference converges to zero in an arbitrarily large disk. Also, we give examples of such matrices.
AB - In 1977, Jacob defines Gα, for any 0 ≤ α < ∞, as the set of all complex sequences x such that lim sup xk 1/k ≤ α. In this paper, we apply Gu - Gv matrix transformation on the sequences of operators given in the famous Walsh's equiconvergence theorem, where we have that the difference of two sequences of operators converges to zero in a disk. We show that the Gu - Gv matrix transformation of the difference converges to zero in an arbitrarily large disk. Also, we give examples of such matrices.
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U2 - 10.1155/IJMMS.2005.2647
DO - 10.1155/IJMMS.2005.2647
M3 - Article
AN - SCOPUS:29144492815
SN - 0161-1712
VL - 2005
SP - 2647
EP - 2653
JO - International Journal of Mathematics and Mathematical Sciences
JF - International Journal of Mathematics and Mathematical Sciences
IS - 16
ER -