A theorem on entire four dimensional summability methods

摘要

This paper introduce the following concept of double entire double sequences. Let x={xk,l} be a double sequence of complex numbers. Then the double sequence {x} is entire provided that∑k,l=0,0∞,∞xk,lpkql<∞for every positive integers p and q. Using this definition I will also introduce the notion Four dimensional entire summability method. The author uses the notions to prove directly necessary and sufficient condition which ensure that a four dimensional transformation is entire.