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 On the almost everywhere statistical convergence of sequences of fuzzy numbers

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2683-2693 ◽  
Author(s):  
Özer Talo
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Almost Everywhere ◽  
Statistical Limit ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

In this paper, we define the concept of almost everywhere statistical convergence of a sequence of fuzzy numbers and prove that a sequence of fuzzy numbers is almost everywhere statistically convergent if and only if its statistical limit inferior and limit superior are equal. To achieve this result, new representations for statistical limit inferior and limit superior of a sequence of fuzzy numbers are obtained and we show that some properties of statistical limit inferior and limit superior can be easily derived from these representations.

scholarly journals Generalized Nörlund and Nörlund-type Means of Sequences of Fuzzy Numbers

2020 ◽  
Vol 13 (5) ◽  
pp. 1088-1096
Author(s):  
Pradosh Kumar Pattanaik ◽  
Susanta Kumar Paikray ◽  
Bidu Bhusan Jena
Keyword(s):  
Fuzzy Numbers ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Slow Oscillation ◽  
Real Numbers ◽  
Fuzzy Real Numbers ◽  
Sequences Of Fuzzy Numbers ◽  
Necessary And Sufficient ◽  
Convergent Sequences

In this article we study some properties of generalized Nörlund and Nörlund-typemeans of sequences of fuzzy real numbers. We establish necessary and sufficient conditions for our purposed methods to transform convergent sequences of fuzzy real numbers into convergent sequences of fuzzy real numbers which also preserve the limit. Finally, we establish some results showing the connection between the generalized N ̈orlund and N ̈orlund-type limits and the usual limits under slow oscillation of sequences of fuzzy real numbers.

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.

ON ALMOST CONVERGENT SEQUENCES OF FUZZY NUMBERS

2006 ◽  
Vol 02 (02) ◽  
pp. 123-130 ◽  
Author(s):  
EKREM SAVAŞ
Keyword(s):  
Metric Space ◽  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Complete Metric Space ◽  
Sequences Of Fuzzy Numbers ◽  
Convergent Sequences

In this paper, we study the space of almost convergent sequences of fuzzy numbers and show that it is complete metric space. We also introduce and discuss the concept of almost statistical convergence of fuzzy numbers.

Sign in / Sign up

Export Citation Format

Share Document