scholarly journals Statistical Convergence of Double Sequences of Order

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
R. Çolak ◽  
Y. Altin
Keyword(s):  
Statistical Convergence ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Real Numbers ◽  
New Approach ◽  
Cesaro Summability

We intend to make a new approach and introduce the concepts of statistical convergence of order and strongly -Cesàro summability of order for double sequences of complex or real numbers. Also, some relations between the statistical convergence of order and strong -Cesàro summability of order are given.

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.

Statistical convergence of double sequences on product time scales

Analysis ◽  
2019 ◽  
Vol 39 (3) ◽  
pp. 71-77 ◽  
Author(s):  
Muhammed Çinar ◽  
Emrah Yilmaz ◽  
Yavuz Altin ◽  
Tuba Gulsen
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Statistical Convergence ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Basic Concepts ◽  
Arbitrary Product

AbstractIn this study, we present the basic concepts of statistical convergence for double sequences on an arbitrary product time scale. Moreover, we investigate the connection between statistical convergence for double sequences and double Cesàro summability on a product time scale.

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.

Applications of Statistical Convergence of order (η, δ + γ) in difference sequence spaces of fuzzy numbers

2020 ◽  
pp. 1-9
Author(s):  
Swati Jasrotia ◽  
Uday Pratap Singh ◽  
Kuldip Raj
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Cesàro Summability ◽  
Matlab Software ◽  
Cesaro Summability ◽  
Set Up ◽  
Difference Sequence Spaces

In this article, we introduce and study some difference sequence spaces of fuzzy numbers by making use of λ-statistical convergence of order (η, δ + γ) . With the aid of MATLAB software, it appears that the statistical convergence of order (η, δ + γ) is well defined every time when (δ + γ) > η and this convergence fails when (δ + γ) < η. Moreover, we try to set up relations between (Δv, λ)-statistical convergence of order (η, δ + γ) and strongly (Δv, p, λ)-Cesàro summability of order (η, δ + γ) and give some compelling instances to show that the converse of these relations is not valid. In addition to the above results, we also graphically exhibits that if a sequence of fuzzy numbers is bounded and statistically convergent of order (η, δ + γ) in (Δv, λ), then it need not be strongly (Δv, p, λ)-Cesàro summable of order (η, δ + γ).

scholarly journals Results on Tauberian Theorem for Cesàro Summable Double Sequences of Fuzzy Numbers

2020 ◽  
Vol 44 (4) ◽  
pp. 495-508 ◽  
Author(s):  
B. B. Jena ◽  
S. K. PAIKRAY ◽  
P. PARIDA ◽  
H. DUTTA
Keyword(s):  
Tauberian Theorem ◽  
Fuzzy Numbers ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Special Cases ◽  
Sequences Of Fuzzy Numbers

The paper aims to establish new results on Tauberian theorem for Cesàro summability of double sequences of fuzzy numbers, and thus to extend and unify several results in the available literature. Further, a number of special cases, corollaries and illustrative example in support of the investigation of this paper are also presented.

scholarly journals A Tauberian Theorem for Double Cesàro Summability Method

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
Bidu Bhusan Jena ◽  
Susanta Kumar Paikray ◽  
Umakanta Misra
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
De La Vallée Poussin

We have generalized Littlewood Tauberian theorems for(C,k,r)summability of double sequences by using oscillating behavior and de la Vallée-Poussin mean. Further, the generalization of(C,r)summability from(C,k,r)summability is given as corollaries which were earlier established by the authors.

scholarly journals Statistical Tauberian theorems for Cesàro integrability mean based on post-quantum calculus

2020 ◽  
Vol 9 (3) ◽  
pp. 653-663
Author(s):  
P. Parida ◽  
S. K. Paikray ◽  
B. B. Jena
Keyword(s):  
Continuous Function ◽  
Statistical Convergence ◽  
Tauberian Theorems ◽  
Cesàro Summability ◽  
Quantum Calculus ◽  
Cesaro Summability ◽  
Single Integral ◽  
De La Vallée Poussin

Abstract The notion of statistical convergence is more general than the classical convergence. Tauberian theorems via different ordinary summability means have been established by many researchers. In the present work, we have established some new Tauberian theorems based on post-quantum calculus via statistical Cesàro summability mean of real-valued continuous function of one variable under oscillating behavior and De la vallée Poussin mean of a single integral. Moreover, some remarks and corollaries are provided here to support our theorems.

scholarly journals On(Δm,I)-Statistical Convergence of Orderα

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Mikail Et ◽  
Abdullah Alotaibi ◽  
S. A. Mohiuddine
Keyword(s):  
Statistical Convergence ◽  
Cesàro Summability ◽  
Cesaro Summability

The idea ofI-convergence of real sequences was introduced by Kostyrko et al., (2000/01) and also independently by Nuray and Ruckle (2000). In this paper, we introduce the concepts of(Δm,I)-statistical convergence of orderαand strong(Δpm,I)-Cesàro summability of orderαof real sequences and investigated their relationship.

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