On General Summability Factor Theorems

On General Summability Factor Theorems

In the recent papers [1, 2], the author obtained necessary and sufficient conditions for a series ∑ an which is absolutely summable of order k by a weighted mean method, 1 < k ≤ s <∞, to be such that anλn is absolutely summable of order s by a triangular matrix method. In this paper, we obtain sufficient and (different) necessary conditions for a series ∑ an which is absolutely summable |A|k to...

Research Article On General Summability Factor Theorems

In the recent papers [1, 2], the author obtained necessary and sufficient conditions for a series ∑ an which is absolutely summable of order k by a weighted mean method, 1 < k ≤ s <∞, to be such that anλn is absolutely summable of order s by a triangular matrix method. In this paper, we obtain sufficient and (different) necessary conditions for a series ∑ an which is absolutely summable |A|k to...

On Some Mercerian Theorems in Summability

Some Theorems on Weighted Mean Summability

In this paper we have proved some theorems on weighted mean summability method by using analytical and summability techniques, which also extends the well known result of Hardy on the Cesàro summability.

Tauberian Theorems for Summability Transforms

we then write sn → s(A), where A is the A method of summability. Appropriate choices of A= [an,k] for n,k ≥ 0 give the classical methods [2]. In this paper, we present various summability analogs of the strong law of large numbers (SLLN) and their rates of convergence in an unified setting, beyond the class of random-walk methods. A convolution summability method introduced in the next section ...