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 (λ,μ) Statistical Convergence of Order γ for Double Sequences of Functions

2018 ◽  
Vol 22 ◽  
pp. 01058
Author(s):  
Muhammed Çınar ◽  
Dilan Şeker ◽  
Mikail Et
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Double Sequences

In this present work, we investigate the concepts of Δr - statistical convergence of order [see formula in PDF] for double sequences of real valued functions. Also some definitions we given for Δr - statistical Cauchy sequence for double sequences of real valued functions and some relations between [see formula in PDF] statistical convergence and strong [see formula in PDF]-summability are given.

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 The backward operator of double almost $\left(\lambda_{m}\mu_{n}\right)$ convergence in $\chi^{2}-$Riesz space defined by a Musielak-Orlicz function

2017 ◽  
Vol 37 (3) ◽  
pp. 85-97
Author(s):  
Nagarajan Subramanian ◽  
Ayhan Esi
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Orlicz Function ◽  
Riesz Space

In this paper we introduce the backward operator is $\nabla$ and study the notion of $\nabla-$ statistical convergence and $\nabla-$ statistical Cauchy sequence using by almost $\left(\lambda_{m}\mu_{n}\right)$ convergence in $\chi^{2}-$Riesz space and also some inclusion theorems are discussed.

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
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