Statistical convergence of order β for double sequences of fuzzy numbers defined by a modulus function

2018 ◽  
Author(s):  
Hıfsı Altınok ◽  
Yavuz Altın ◽  
Mahmut Işık
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Modulus Function ◽  
Double Sequences ◽  
Sequences Of Fuzzy Numbers

scholarly journals Generalized Weighted Statistical Convergence for Double Sequences of Fuzzy Numbers and Associated Korovkin-Type Approximation Theorem

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Abdullah Alotaibi
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Approximation Theorem ◽  
Bernstein Operators ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Functions Of Two Variables ◽  
Sequences Of Fuzzy Numbers ◽  
Bivariate Functions

We define the notions of weighted λ,μ-statistical convergence of order γ1,γ2 and strongly weighted λ,μ-summability of γ1,γ2 for fuzzy double sequences, where 0<γ1,γ2≤1. We establish an inclusion result and a theorem presenting a connection between these concepts. Moreover, we apply our new concept of weighted λ,μ-statistical convergence of order γ1,γ2 to prove Korovkin-type approximation theorem for functions of two variables in a fuzzy sense. Finally, an illustrative example is provided with the help of q-analogue of fuzzy Bernstein operators for bivariate functions which shows the significance of our approximation theorem.

scholarly journals Tauberian theorems for weighted mean statistical summability of double sequences of fuzzy numbers

2021 ◽  
Vol 25 (2) ◽  
pp. 175-187
Author(s):  
Hemen Dutta ◽  
Jyotishmaan Gogoi
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Weighted Mean ◽  
Tauberian Conditions ◽  
Weighted Means ◽  
Sequences Of Fuzzy Numbers

We discuss Tauberian conditions under which the statistical convergence of double sequences of fuzzy numbers follows from the statistical convergence of their weighted means. We also prove some other results which are necessary to establish the main results.

Statistical Convergence of order β for (λ, μ) double sequences of fuzzy numbers

2020 ◽  
Vol 39 (5) ◽  
pp. 6949-6954
Author(s):  
Damla Barlak
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Double Sequences ◽  
Sequences Of Fuzzy Numbers

In this study, we introduce the concepts of φλ,μ-double statistically convergence of order β in fuzzy sequences and strongly λ- double Cesaro summable of order β for sequences of fuzzy numbers. Also we give some inclusion theorems.

Applications of deferred Cesàro statistical convergence of sequences of fuzzy numbers of order (ξ, ω)

2021 ◽  
pp. 1-10
Author(s):  
Sonali Sharma ◽  
Uday Pratap Singh ◽  
Kuldip Raj
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Matlab Software ◽  
Difference Sequences ◽  
Cesaro Summability ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers ◽  
Theoretical Results

The purpose of this article is to study deferred Cesrào statistical convergence of order (ξ, ω) associated with a modulus function involving the concept of difference sequences of fuzzy numbers. The study reveals that the statistical convergence of these newly formed sequence spaces behave well for ξ ≤ ω and convergence is not possible for ξ > ω. We also define p-deferred Cesàro summability and establish several interesting results. In addition, we provide some examples which explain the validity of the theoretical results and the effectiveness of constructed sequence spaces. Finally, with the help of MATLAB software, we examine that if the sequence of fuzzy numbers is bounded and deferred Cesàro statistical convergent of order (ξ, ω) in (Δ, F, f), then it need not be strongly p-deferred Cesàro summable of order (ξ, ω) in general for 0 < ξ ≤ ω ≤ 1.

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