136 research outputs found
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
Tauberian theorems for weighted mean statistical summability of double sequences of fuzzy numbers
We discuss Tauberian conditions under which the statistical convergence of double sequences of fuzzy numbers follows from the statistical convergence of their weighted means. We also prove some other results which are necessary to establish the main results
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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