A Note on Generalized |A|k-Summability Factors for Infinite Series
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چکیده
Aweighted mean matrix, denoted by N,pn , is a lower triangular matrix with entries pk/Pn, where {pk} is a nonnegative sequence with p0 > 0, and Pn : ∑n k 0 pk. Mishra and Srivastava 1 obtained sufficient conditions on a sequence {pk} and a sequence {λn} for the series ∑ anPnλn/npn to be absolutely summable by the weighted mean matrix N,pn . Recently Savaş and Rhoades 2 established the corresponding result for a nonnegative triangle, using the correct definition of absolute summability of order k ≥ 1. Let A be an infinite lower triangular matrix. We may associate with A two lower triangular matrices A and Â, whose entries are defined by
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