Weighted (λ,μ)-statistical convergence and statistical summability methods of double sequences of fuzzy numbers with application to Korovkin-type fuzzy approximation theorem

2021 ◽  
Author(s):  
Jyotishmaan Gogoi ◽  
Hemen Dutta
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Approximation Theorem ◽  
Double Sequences ◽  
Fuzzy Approximation ◽  
Summability Methods ◽  
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.

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.

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.

scholarly journals On statistical summability (N¯,P) of sequences of fuzzy numbers

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 873-884 ◽  
Author(s):  
Özer Talo ◽  
Canan Balb
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Tauberian Conditions ◽  
Sequences Of Fuzzy Numbers

In this paper we introduce the concept of statistical summability (N?,p) of sequences of fuzzy numbers. We also present Tauberian conditions under which statistical convergence of a sequence of fuzzy numbers follows from its statistical summability (N?,p). Furthermore, we prove a Korovkin-type approximation theorem for fuzzy positive linear operators by using the notion of statistical summability (N?,p).

Sign in / Sign up

Export Citation Format

Share Document