scholarly journals Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers

2017 ◽  
Vol 15 (1) ◽  
pp. 157-178 ◽  
Author(s):  
Zerrin Önder ◽  
İbrahim Çanak ◽  
Ümit Totur
Keyword(s):  
Fuzzy Numbers ◽  
Double Sequence ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Sequences Of Fuzzy Numbers

Abstract In this paper, we prove that a bounded double sequence of fuzzy numbers which is statistically convergent is also statistically (C, 1, 1) summable to the same number. We construct an example that the converse of this statement is not true in general. We obtain that the statistically (C, 1, 1) summable double sequence of fuzzy numbers is convergent and statistically convergent to the same number under the slowly oscillating and statistically slowly oscillating conditions in certain senses, respectively.

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 Regularly -Convergence and Regularly -Cauchy Double Sequences of Fuzzy Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Erdinç Dündar ◽  
Özer Talo ◽  
Feyzi Başar
Keyword(s):  
Fuzzy Numbers ◽  
Double Sequence ◽  
Double Sequences ◽  
Sequences Of Fuzzy Numbers

In this paper, we introduce the notions of regularly , -convergence and regularly , -Cauchy double sequence of fuzzy numbers. Also, we study some properties of these concepts.

Applications of Tauberian theorems for double sequences of fuzzy numbers via De La Vallée Poussin mean

2021 ◽  
pp. 1-10
Author(s):  
Anu Choudhary ◽  
Kuldip Raj ◽  
M. Mursaleen
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Double Sequence ◽  
Double Difference ◽  
Tauberian Theorems ◽  
Tauberian Conditions ◽  
Hardy Type ◽  
Number Sequences ◽  
Sequences Of Fuzzy Numbers ◽  
De La Vallée Poussin

Tauberian theorem serves the purpose to recuperate Pringsheim’s convergence of a double sequence from its (C, 1, 1) summability under some additional conditions known as Tauberian conditions. In this article, we intend to introduce some Tauberian theorems for fuzzy number sequences by using the de la Vallée Poussin mean and double difference operator of order r . We prove that a bounded double sequence of fuzzy number which is Δ u r - convergent is ( C , 1 , 1 ) Δ u r - summable to the same fuzzy number L . We make an effort to develop some new slowly oscillating and Hardy-type Tauberian conditions in certain senses employing de la Vallée Poussin mean. We establish a connection between the Δ u r - Hardy type and Δ u r - slowly oscillating Tauberian condition. Finally by using these new slowly oscillating and Hardy-type Tauberian conditions, we explore some relations between ( C , 1 , 1 ) Δ u r - summable and Δ u r - convergent double fuzzy number 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.

Sign in / Sign up

Export Citation Format

Share Document