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We obtain sufficient and (different) necessary conditions for the series a₍, which is absolutely summable of order k by a triangular matrix method A, to be such that a₍ₙ is absolutely summable of order k by a triangular matrix B. As corollaries we obtain a number of inclusion theorems. 2000 Mathematics Subject Classification. Primary: 40G99; Secondary: 40G05, 40D15
Rhoades et al. (Wed,) studied this question.