Statistical Convergence of Double Sequences

By Mursaleen, O. H. Edely. 2003

598 citations recorded by the source corpus.

The idea of statistical convergence was first introduced by Fast (1951) but the rapid developments were started after the papers of Salat (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 Cesaro summable double sequences.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3d1d965b78783b3734aab9c779283f8956dcd8e5

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In Applied Mathematics

In Numerical Analysis

In Statistics and Probability

Citations in the corpus

On I and I ∗ −convergence of double sequences (2007, unknown): “Key words: statistical convergence, I-convergence, I-Cauchy sequences, double sequences AMS subject classifications: 40A05 Received March 10, 2007 Accepted May 19, 2007”
The semi normed space defined by a double gai sequence of modulus function (2010, unknown): “Nextly, Mursaleen [26] and Mursaleen and Edely [27] have defined the almost strong regularity of matrices for double sequences and applied these matrices to establish a core theorem and introduced the M −core for double sequences and determined those four dimensional matrices transforming every boun”
Restricting statistical convergence (2012, methodology): “In [ 13 ] Mursaleen et al showed that a sequence {xij} i,j∈N is statistically convergent to L (i.e.”
On ideal convergence of double sequences in probabilistic normed spaces (2011, background): “We also define ∮ -Cauchy and ∮ - Cauchy double sequences on PN spaces and show that ∮ -convergent double sequences are ∮ -Cauchy on these spaces.”
Lacunary statistical convergence in random 2-normed spaces (2012, unknown): “[4,5,8,10,15,18, 23].”
Generalized statistical convergence and statistical core of double sequences (2010, background): “Then, clearly x is bounded and x ∈ [C, 1, 1] and hence, by Theorem 4.1 (a) of [ 14 ], x ∈ S2 .B ut on the other hand, x �∈ [V, λ, μ ]a nd from Theorem 2.9,x �∈ S ∞ ; a contradiction and hence (2.1)”
Korovkin type approximation theorem for functions of two variables in statistical sense (2010, background): “coincides with the notion of statistical convergence for double sequence, which was introduced in ([10], [ 11 ]).”
On ideal convergence in probabilistic normed spaces (2012, background): “The concept of statistical convergence for sequences of real numbers was introduced by Fast [4] and Steinhaus [22] independently in the same year 1951 and since then several generalizations and applications of this notion have been investigated by various authors, namely [3], [7], [15], [16], [17], ”