GENERAL CONTROL MODULO AND TAUBERIAN REMAINDER THEOREMS FOR (C, 1) 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 ...

Tauberian Theorems by Weighted Summability Method

A Tauberian Theorem for (C, 1) Summability Method

In this paper, we retrieve slow oscillation of a real sequence u = (u n) out of (C, 1) summability of the generator sequence (V (0) n (Δu)) of (u n) under some additional condition. Consequently, we recover convergence or subsequential convergence of (u n) out of (C, 1) summability of (u n) under certain additional conditions that control oscillatory behavior of the sequence (u n).

On Tauberian Conditions for (c, 1) Summability of Integrals

We investigate some Tauberian conditions in terms of the general control modulo of the oscillatory behavior of integer order of continuous real functions on [0,∞) for (C, 1) summability of integrals. Moreover, we obtain a Tauberian theorem for a real bounded function on [0,∞).

One-sided Tauberian Theorems for Dirichlet Series Methods of Summability

We extend recently established two-sided or O-Tauberian results concerning the summability method Dλ,a based on the Dirichlet series ∑ ane−λnx to one-sided Tauberian results. More precisely, we formulate one-sided Tauberian conditions, under which Dλ,a-summability implies convergence. Our theorems contain various known results on power series methods of summability and, in the so-called high in...