We consider the summability of oneand multi-dimensional trigonometric Fourier series. The Fejér and Riesz summability methods are investigated in detail. Different types of summation and convergence are considered. We will prove that the maximal operator of the summability means is bounded from the Hardy space Hp to Lp, for all p > p0, where p0 depends on the summability method and the dimensio...

Let $(u_n)$ be a sequence of fuzzy numbers.  We recover the slow oscillation of $(u_n)$ of fuzzy numbers from the Ces`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. Further, fuzzy analogues of some well known classical Tauberian theorems for Ces`{a}ro summability method are established as particular cases.

In the present paper, using result of Bennett [1] on characterization factorable matrices, we give necessary and sufficient conditions in order that Σλ_{n}x_{n} is summable |R,p_{n}|_{s} whenever Σμ_{n}x_{n} |C,0|_{k}, |C,0|_{s} |R,p_{n}|_{r},. where 1

Correspondence should be addressed to E. Savaş, [email protected] Received 23 June 2010; Revised 3 September 2010; Accepted 15 September 2010 Academic Editor: J. Szabados Copyright q 2010 E. Savaş. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work ...

let $(u_n)$ be a sequence of fuzzy numbers.  we recover the slow oscillation of $(u_n)$ of fuzzy numbers from the ces`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. further, fuzzy analogues of some well known classical tauberian theorems for ces`{a}ro summability method are established as particular cases.

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...

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 ...