equiconvergence theorem
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2005 ◽  
Vol 2005 (16) ◽  
pp. 2647-2653 ◽  
Author(s):  
Chikkanna R. Selvaraj ◽  
Suguna Selvaraj

In 1977, Jacob definesGα, for any0≤α<∞, as the set of all complex sequencesxsuch that|xk|1/k≤α. In this paper, we applyGu−Gvmatrix 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 theGu−Gvmatrix transformation of the difference converges to zero in an arbitrarily large disk. Also, we give examples of such matrices.


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