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

Orlicz–Pettis Theorem through Summability Methods

This paper unifies several versions of the Orlicz–Pettis theorem that incorporate summability methods. We show that a series is unconditionally convergent if and only if the series is weakly subseries convergent with respect to a regular linear summability method. This includes results using matrix summability, statistical convergence with respect to an ideal, and other variations of summability methods

On Diluted Cesàro Matrices

Bu çalışmada, serilerin üst yakınsaklığı ile bu serilerin kısmi toplamlar dizisinin toplanabilir bir uzanımının varlığı arasında bağlantı kuran bir genel toplanabilme matrisi tanıtıldı. Bu matrislerin bazı özellikleri ve Riesz Matrislerinin hangi koşullar altında bu matris sınıfına girdiği incelendi.In this paper, we introduced some general summability matrices which make contact between the overconvergence of series and the existence of a summable elongation of the sequence of the partial sums of the series. We investigated some properties of them and analysed under what conditions will the Riesz Matrices be in the class of matrices which are defined

Ideal Convergence and Completeness of a Normed Space

We aim to unify several results which characterize when a series is weakly unconditionally Cauchy (wuc) in terms of the completeness of a convergence space associated to the wuc series. If, additionally, the space is completed for each wuc series, then the underlying space is complete. In the process the existing proofs are simplified and some unanswered questions are solved. This research line was originated in the PhD thesis of the second author. Since then, it has been possible to characterize the completeness of a normed spaces through different convergence subspaces (which are be defined using different kinds of convergence) associated to an unconditionally Cauchy sequence