Tauberian theorems for the product of borel and logarithmic methods of summability

Abstract

In this paper, we show that if a sequence is summable by the product method (B)(l, k), then it is also summable by the logarithmic method (l, k), provided two-sided conditions of Hardy-type are satisfied. We also obtain some classical Tauberian theorems and their generalizations as special cases of our main theorems.