This paper is a study of summability methods that are based on Dirichlet convolution. If f(n) is a function on positive integers and x is a sequence such that limn→∞ Σk≤n 1/k(f * x)(k) = L, then x is said to be Af-summable to L. The necessary and sufficient condition for the matrix Af to preserve bounded variation of sequences is established. Also, the matrix Af is investigated as l - l and G - G mappings. The strength of the Af-matrix is also discussed.
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