Statistical Convergence of Double Sequences

2014 ◽  
pp. 117-132 ◽  
Author(s):  
M. Mursaleen ◽  
S. A. Mohiuddine
Keyword(s):  
Statistical Convergence ◽  
Double Sequences

scholarly journals Statistical convergence of double sequences on probabilistic normed spaces defined by $[ V, \lambda, \mu ]$-summability

2014 ◽  
Vol 33 (2) ◽  
pp. 59-67
Author(s):  
Pankaj Kumar ◽  
S. S. Bhatia ◽  
Vijay Kumar
Keyword(s):  
Statistical Convergence ◽  
Convergence Criteria ◽  
Double Sequences ◽  
Normed Spaces ◽  
Real Numbers ◽  
Positive Real ◽  
Probabilistic Normed Spaces

In this paper, we aim to generalize the notion of statistical convergence for double sequences on probabilistic normed spaces with the help of two nondecreasing sequences of positive real numbers $\lambda=(\lambda_{n})$ and $\mu = (\mu_{n})$  such that each tending to zero, also $\lambda_{n+1}\leq \lambda_{n}+1, \lambda_{1}=1,$ and $\mu_{n+1}\leq \mu_{n}+1, \mu_{1}=1.$ We also define generalized statistically Cauchy double sequences on PN space and establish the Cauchy convergence criteria in these spaces.

Deferred Cesàro summability and statistical convergence for double sequences of sets

2021 ◽  
pp. 1-9
Author(s):  
Uğur Ulusu ◽  
Esra Gülle
Keyword(s):  
Statistical Convergence ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Cesàro Mean ◽  
Cesaro Summability ◽  
Cesaro Mean

The main purpose of this paper is introduced the concept of deferred Cesàro mean in the Wijsman sense for double sequences of sets and then presented the concepts of strongly deferred Cesàro summability and deferred statistical convergence in the Wijsman sense for double sequences of sets. Also, investigate the relationships between these concepts and then to prove some theorems associated with the concepts of deferred statistical convergence in the Wijsman sense for double sequences of sets is purposed.

scholarly journals Lacunary statistical convergence of double sequences of sets

2015 ◽  
Vol 20 (7) ◽  
pp. 2883-2888 ◽  
Author(s):  
Fatih Nuray ◽  
Uğur Ulusu ◽  
Erdinç Dündar
Keyword(s):  
Statistical Convergence ◽  
Double Sequences ◽  
Lacunary Statistical Convergence

Generalized statistical convergence and statistical core of double sequences

2010 ◽  
Vol 26 (11) ◽  
pp. 2131-2144 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Celal Çakan ◽  
Syed Abdul Mohiuddine ◽  
Ekrem Savaş
Keyword(s):  
Statistical Convergence ◽  
Double Sequences

scholarly journals Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Double Sequence ◽  
Finite Measure ◽  
Measurable Space ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α -level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.

scholarly journals DELTA^m STATISTICAL CONVERGENCE OF ORDER alpha FOR DOUBLE SEQUENCES OF FUNCTIONS

2020 ◽  
pp. 393
Author(s):  
Muhamed Çinar ◽  
Mikail Et
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Double Sequences

In this paper, we introduce and examine the concepts of Delta^m pointwise and Delta^m uniform statistical convergence of order alpha for double sequences of real valued functions. Also we give the concept of Delta^m statistically Cauchy sequence for double sequences of real valued functions and prove that it is equivalent to Delta^m pointwise statistical convergence of order alpha for double sequences of real valued functions. Also some relations between S_alpha^ 2(Delta^m,f )-statistical convergence and strong [w_p^2]_alpha (Delta^m,f )-summability are given.

scholarly journals f-LACUNARY STATISTICAL CONVERGENCE AND STRONG f-LACUNARY SUMMABILITY OF ORDER α OF DOUBLE SEQUENCES

2020 ◽  
pp. 495
Author(s):  
Hacer Sengul ◽  
Mikail Et ◽  
Yavuz Altın
Keyword(s):  
Statistical Convergence ◽  
Double Sequences ◽  
Lacunary Statistical Convergence ◽  
Inclusion Relations

The main object of this article is to introduce the concepts of f-lacunary statistical convergence of order alpha and strong f-lacunary summability of order alpha of double sequences and give some inclusion relations between these concepts.

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