Statistical Convergence Of Double Sequences Research Articles

A NOTE ON LACUNARY STATISTICALLY CONVERGENT DOUBLE SEQUENCES OF FUZZY NUMBERS

In this paper we introduce and study lacunary statistical convergence for double sequences of fuzzy numbers and we shall also present some inclusion theorems.

Statistical convergence of double sequences of real-valued functions

In this study, we introduce the notion of pointwise and uniform statistical convergence of double sequences of real-valued functions. We also give the relations between these convergences and pointwise,uniform convergence. Furthermore, we introduce the concept of statistically Cauchy sequence and study statistical analogue of convergence and Cauchy criterion for double sequences of real-valued functions.

Lacunary statistical convergence of multiple sequences

Quite recently, Mursaleen and Edely [M. Mursaleen, O.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. (in press)], defined the statistical analogue for double sequences x = { x k , l } as follows: A real double sequence x = { x k , l } is said to be P-statistically convergent to L provided that for each ϵ > 0 P − lim m , n 1 m n { numbers of ( j , k ) : j < m and k < n , | x j , k − L | ≥ ϵ } . In this paper we introduce and study lacunary statistical convergence for double sequences and we shall also present some inclusion theorems.

Tauberian theorems for statistically convergent double sequences

In [F. Moricz, Tauberian theorems for Cesàro summable double sequences, Studia Math. 110 (1994) 83–96], Moricz has proved some Tauberian theorems for Cesàro summable double sequences and deduced the Tauberian theorems of Landau [E. Landau, Über die Bedeutung einiger neuerer Grenzwertsätze der Herren Hardy and Axer, Prac. Mat.-Fiz. 21 (1910) 97–177] and Hardy [G.H. Hardy, Divergent Series, Univ. Press, Oxford 1956] type. In [J.A. Fridy, M.K. Khan, Statistical extension of some classical Tauberian theorems, Proc. Amer. Math. Soc. 128 (2000) 2347–2355], Fridy and Khan have given statistical extensions of some classical Tauberian theorems. The concept of statistical convergence for double sequences has recently been introduced by Mursaleen and Edely [M. Mursaleen, Osama H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003) 223–231] and by Moricz [F. Moricz, Statistical convergence of multiple sequences, Arch. Math. 81 (2003) 82–89] independently. In this paper we give some Tauberian theorems for statistically convergent double sequences. We have also provided some examples including an example to Problem 1 of Moricz [F. Moricz, Tauberian theorems for Cesàro summable double sequences, Studia Math. 110 (1994) 83–96].

Regular statistical convergence of double sequences

Regular statistical convergence of double sequences

On some double almost lacunary sequence spaces defined by Orlicz functions

In this paper we introduce a new concept for almost lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space. We also introduce and study almost lacunary statistical convergence for double sequences and we shall also present some inclusion theorems.

Statistical convergence of double sequences

The idea of statistical convergence was first introduced by Fast (1951) but the rapid developments were started after the papers of Šalát (1980) and Fridy (1985). Now a days it has become one of the most active area of research in the field of summability. In this paper we define and study statistical analogue of convergence and Cauchy for double sequences. We also establish the relation between statistical convergence and strongly Cesàro summable double sequences.