Tauberian theorems for Abel summability of sequences of fuzzy numbers

2015 ◽  
Author(s):  
Enes Yavuz ◽  
Hüsamettin Çoşkun
Keyword(s):  
Fuzzy Numbers ◽  
Tauberian Theorems ◽  
Abel Summability ◽  
Sequences Of Fuzzy Numbers

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.

Abel summability of sequences of fuzzy numbers

2014 ◽  
Vol 20 (3) ◽  
pp. 1041-1046 ◽  
Author(s):  
Enes Yavuz ◽  
Özer Talo
Keyword(s):  
Fuzzy Numbers ◽  
Abel Summability ◽  
Sequences Of Fuzzy Numbers

scholarly journals Tauberian theorems for statistically (C,1)-convergent sequences of fuzzy numbers

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 849-858 ◽  
Author(s):  
Özer Talo ◽  
Celal Çakan
Keyword(s):  
Fuzzy Numbers ◽  
Bounded Sequence ◽  
Tauberian Theorems ◽  
Tauberian Conditions ◽  
Statistical Limit ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers ◽  
Necessary And Sufficient ◽  
Convergent Sequences

In this paper, we have determined necessary and sufficient Tauberian conditions under which statistically convergence follows from statistically (C,1)-convergence of sequences of fuzzy numbers. Our conditions are satisfied if a sequence of fuzzy numbers is statistically slowly oscillating. Also, under additional conditions it is proved that a bounded sequence of fuzzy numbers which is (C,1)-level-convergent to its statistical limit superior is statistically convergent.

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.

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.

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