200 research outputs found
Voronoi means, moving averages, and power series
We introduce a {\it non-regular} generalisation of the N\"{o}rlund mean, and
show its equivalence with a certain moving average. The Abelian and Tauberian
theorems establish relations with convergent sequences and certain power
series. A strong law of large numbers is also proved
Comparison theorems for summability methods of sequences of fuzzy numbers
In this study we compare Ces\`{a}ro and Euler weighted mean methods of
summability of sequences of fuzzy numbers with Abel and Borel power series
methods of summability of sequences of fuzzy numbers. Also some results dealing
with series of fuzzy numbers are obtained.Comment: publication information is added, typos correcte
Extended Tauberian Theorem for the weighted mean Method of Summability
We prove a new Tauberian-like theorem that establishes the slow oscillation of a real sequence u = (un) on the basis of the weighted mean summability of its generator sequence and some conditions.Доведено нову теорему тауберового типу, яка встановлює повільні коливання дійсної послідовності u = (u n )) на основі збіжності її генеруючої послідовності у зважених середніх та певних умов
TAUBERIAN THEOREMS FOR THE WEIGHTED MEAN METHOD OF SUMMABILITY OF INTEGRALS
Let be a positive weight function on which is integrable in Lebesgue's sense over every finite interval for , and as .Given a real or complex-valued function , we define andprovided that . We say that is summable to by the -th iteration of weighted mean method determined by the function , or for short, integrable to a finite number ifIn this case, we write . It is known thatif the limit exists, then also exists. However, the converse of this implicationis not always true. Some suitable conditions together with the existence of the limit , which is so called Tauberian conditions, may imply convergence of . In this paper, one- and two-sided Tauberian conditions in terms of the generating function and its generalizations for summable integrals of real- or complex-valued functions have been obtained. Some classical type Tauberian theorems given for Ces\`{a}ro summability and weighted mean method of summability have been extended and generalized.
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