TAUBERIAN THEOREMS FOR THE PRODUCT OF BOREL AND LOGARITHMIC METHODS OF SUMMABILITY

S. A. SEZER

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Abstract

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

Keywords

Tauberian theorems, Borel summability, logarithmic summability, Hardytype conditions.