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

Some Cesàro-Type Summability and Statistical Convergence of Sequences Generated by Fractional Difference Operator

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Some Generalized Difference Cesàro Double Sequence Space of Fuzzy Real Number Defined by Double Orlicz Function

في هذا البحث قدمنا بعض تعميم اختلاف  لفضاءات المتتابعات الثنائية من الاعداد  الحقيقية   الضبابية  المعرفة بواسطة دالة  أورليسز المضاعفة. وندرس خصائصها المختلفة مثل الكمال والصلابة والتناظر وما إلى ذلك. كما حصلنا على بعض علاقة التضمين التي تتضمن فضاء المتتابعات الثنائيةIn this paper we introduce some generalized difference Cesàro double sequence space of fuzzy real number by using double orlicz function . and we study their different properties like completeness , solidity, symmwtricity etc. . Also we obtain some inclusion relation involving these double sequence space

Wijsman ptrongly p-Cesàro summability and Wijsman statistical convergence of order α for double set sequences

The concept of statistical convergence was introduced by Steinhaus (1951) and Fast (1951), and later reintroduced by Schoenberg (1959) independently. Then, many researchers have studied on this concept until recently (see Connor 1988; Fridy 1985; Šalát 1980; Tripathy 1998). The order of statistical convergence of a single sequence of numbers was given by Gadjiev and Orhan (2001). Then, the concepts of statistical convergence of order α and strongly p-Cesàro summability of order α were studied by Çolak (2010) and Çolak and Bektaş (2011). In 1900, Pringsheim introduced the concept of convergence for double sequences. Recently, Mursaleen and Edely (2003) extended this concept to statistical convergence. More developments on double sequences can be found in Çakallı and Savaş (2010), Mohiuddine et al. (2012) and Bhunia et al. (2012). Very recently, the concepts of statistical convergence of order α and strongly p-Cesàro summability of order α for double sequences were studied by Savaş (2013) and Çolak and Altın (2013). The concept of convergence for number sequences was transferred to the concepts of convergence for set sequences by many authors. In this study, the concept of Wijsman convergence which is one of these transfers is considered (see Baronti and Papini 1986; Beer 1985, 1994; Wijsman 1964). Nuray and Rhoades (2012) extended the concept of Wijsman convergence to statistical convergence for set sequences and gave some basic theorems. Very recently, the concept of Wijsman I-statistical convergence of order α was studied by Savaş (2015) and Şengül and Et (2017). Nuray et al. (2014) introduced the concepts of Wijsman convergence and Wijsman strongly p-Cesàro summability for double set sequences. Also, the concept of Wijsman statistical convergence was studied by Nuray et al. (2019). In this study, we introduce the concepts of Wijsman strongly p-Cesàro summability of order α and Wijsman statistical convergence of order α for double set sequences. Also, we investigate some properties of these concepts and examine the relationship between them.hoenberg (1959) tarafından yeniden tanımlanmıştır. Yakın zamana kadar pek çok araştırmacı da bu kavram üzerine çalışmıştır (bkz Connor 1988; Fridy 1985; Šalát 1980; Tripathy 1998). Reel sayı dizilerinin istatistiksel yakınsaklık mertebesi Gadjiev ve Orhan (2001) tarafından verilmiştir. Daha sonra Çolak (2010) ve Çolak ve Bektaş (2011) tarafından .... mertebeden istatistiksel yakınsaklık ve .... mertebeden kuvvetli ...-Cesàro toplanabilirlik kavramları çalışılmıştır. Pringsheim 1900 de çift diziler için yakınsaklık kavramını tanıtmıştır. Mursaleen ve Edely (2003) bu kavramı istatistiksel yakınsaklığa genişletmiştir. Çift diziler üzerine yapılan pek çok çalışma Çakallı ve Savaş (2010), Mohiuddine vd. (2012) ve Bhunia vd. (2012) de bulunabilir. Son zamanlarda, çift diziler için .... mertebeden istatistiksel yakınsaklık ve .... mertebeden kuvvetli ...-Cesàro toplanabilirlik kavramları Savaş (2013) ve Çolak ve Altın (2013) tarafından çalışılmıştır. Sayı dizileri için yakınsaklık kavramı pek çok araştırmacı tarafından küme dizileri için yakınsaklık kavramlarına aktarılmıştır. Bu çalışmada, küme dizileri için Wijsman yakınsaklık kavramı ele alınmıştır (bkz Baronti ve Papini 1986; Beer 1985, 1994; Wijsman 1964). Nuray ve Rhoades (2012) küme dizileri için Wijsman istatistiksel yakınsaklık kavramını çalışmış ve bazı temel teoremleri vermiştir. Son zamanlarda, .... mertebeden Wijsman ...-istatistiksel yakınsaklık kavramı Savaş (2015) ve Şengül ve Et (2017) tarafından çalışılmıştır. Nuray vd. (2014) çift küme dizileri için Wijsman yakınsaklık ve Wijsman kuvvetli ....-Cesàro toplanabilirlik kavramlarını tanıtmıştır. Ayrıca, Wijsman istatistiksel yakınsaklık kavramı Nuray vd. (2019) tarafından incelenmiştir. Bu çalışmada, çift küme dizileri için .... mertebeden Wijsman kuvvetli ...-Cesàro toplanabilirlik ve .... mertebeden Wijsman istatistiksel yakınsaklık kavramları tanıtılmıştır. Ayrıca, bu kavramların bazı özellikleri araştırılmış ve bunlar arasındaki ilişki incelenmiştir

On statistical convergence and strong Cesàro convergence by moduli

In this paper we will establish a result by Connor, Khan and Orhan (Analysis 8:47–63, 1988; Publ. Math. (Debr.) 76:77–88, 2010) in the framework of the statistical convergence and the strong Cesàro convergence defined by a modulus function f . Namely, for every modulus function f , we will prove that a f -strongly Cesàro convergent sequence is always f -statistically convergent and uniformly integrable. The converse of this result is not true even for bounded sequences. We will characterize analytically the modulus functions f for which the converse is true. We will prove that these modulus functions are those for which the statistically convergent sequences are f -statistically convergent, that is, we show that Connor–Khan–Orhan’s result is sharp in this sense

Lacunary statistical convergence of double sequences of sets

In this paper, we study the concepts of Wijsman statistical convergence, Wijsman lacunary statistical convergence, Wijsman lacunary convergence and Wijsman strongly lacunary convergence double sequences of sets and investigate the relationship among them

(R1958) On Deferred Statistical Convergence of Fuzzy Variables

In this paper, within framework credibility theory, we examine several notions of convergence and statistical convergence of fuzzy variable sequences. The convergence of fuzzy variable sequences such as the notion of convergence in credibility, convergence in distribution, convergence in mean, and convergence uniformly virtually certainly via postponed Cesàro mean and a regular matrix are researched using fuzzy variables. We investigate the connections between these concepts. Significant results on deferred statistical convergence for fuzzy variable sequences are thoroughly investigated

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