Asymptotically ideal invariant equivalence

In this paper, the concepts of asymptotically I_σ-equivalence, σ-asymptotically equivalence, strongly σ-asymptotically equivalence and strongly σ-asymptotically p-equivalence for real number sequences are defined. Also, we give relationships among these new type equivalence concepts and the concept of S_σ-asymptotically equivalence which is studied in [Savaş, E. and Patterson, R.F., σ-asymptotically lacunary statistical equivalent sequences, Cent. Eur. J. Math., 4 (2006), No. 4, 648–655

Asymptotically ideal invariant equivalence

In this study, the concepts of asymptotically I_σ-equivalence, σ-asymptotically equivalence, strongly σ-asymptotically equivalence and strongly σ-asymptotically p-equivalence for real number sequences are defined. Also, we give some relationships among this new type equivalence concepts and the concept of S_σ-asymptotically equivalence which is studied in this area befor

Quasi-almost convergence of sequences of sets

In this paper, we defined concepts of Wijsman quasi-almost convergence and Wijsman quasi-almost statistically convergence. Also we give the concepts of Wijsman quasi-strongly almost convergence and Wijsman quasi q-strongly almost convergence. Then, we study relationship among these concepts. Furthermore, we investigate relationship between these concepts and some convergence types given earlier for consequences of sets, as wel

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 some asymptotically equivalence types for double sequences and relations among them

In this study, we give definitions of asymptotically lacunary invariant equivalence, strongly asymptotically lacunary invariant equivalence and asymptotically lacunary ideal invariant equivalence for double sequences. We also examine the existence of some relations among these new equivalence definition

Some asymptotically equivalence types for sequences of sets

In this study, the concepts of asymptotically ideal Cesàro equivalence are defined and the relationships among the concepts of asymptotically strongly ideal Cesàro equivalence, asymptotically strongly ideal lacunary equivalence, asymptotically p-strongly ideal Cesàro equivalence and asymptotically ideal statistical equivalence of sequences of sets are investigated

Asymptotically I_2-lacunary statistical equivalence of double sequences of sets

In this paper, we introduce the concepts of Wijsman I_2-asymptotically statistical equivalence, Wijsman strongly I_2-asymptotically lacunary equivalence and Wijsman I_2-asymtotically lacunary statistical equivalence of double sequences of sets and investigate the relationship between the

On strongly lacunary summability of sequences of sets

In this paper, we introduce the concept of Wijsman strongly lacunary summability for set sequences. Then, we discus its relation with Wijsman strongly Ces`aro summability. Furthermore, we also give its relation with Wijsman almost convergenc