Double summability factor theorems and applications

Weobtain sufficient conditions for the series ∑∑ amn , which is absolutely summable of order k by a double triangular matrix method A , to be such that ∑∑ amnλmn is absolutely summable of order k by a double triangular matrix B . As corollaries we obtain a number of inclusion theorems. Mathematics subject classification (2000): 40G99, 40G05, 40D15.