Tauberian theorems for Cesàro summability of sequences of fuzzy numbers

2014 ◽  
Vol 27 (2) ◽  
pp. 937-942 ◽  
Author(s):  
İbrahim Çanak
Keyword(s):  
Fuzzy Numbers ◽  
Tauberian Theorems ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Sequences Of Fuzzy Numbers

scholarly journals Results on Tauberian Theorem for Cesàro Summable Double Sequences of Fuzzy Numbers

2020 ◽  
Vol 44 (4) ◽  
pp. 495-508 ◽  
Author(s):  
B. B. Jena ◽  
S. K. PAIKRAY ◽  
P. PARIDA ◽  
H. DUTTA
Keyword(s):  
Tauberian Theorem ◽  
Fuzzy Numbers ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Special Cases ◽  
Sequences Of Fuzzy Numbers

The paper aims to establish new results on Tauberian theorem for Cesàro summability of double sequences of fuzzy numbers, and thus to extend and unify several results in the available literature. Further, a number of special cases, corollaries and illustrative example in support of the investigation of this paper are also presented.

Applications of Statistical Convergence of order (η, δ + γ) in difference sequence spaces of fuzzy numbers

2020 ◽  
pp. 1-9
Author(s):  
Swati Jasrotia ◽  
Uday Pratap Singh ◽  
Kuldip Raj
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Cesàro Summability ◽  
Matlab Software ◽  
Cesaro Summability ◽  
Set Up ◽  
Difference Sequence Spaces

In this article, we introduce and study some difference sequence spaces of fuzzy numbers by making use of λ-statistical convergence of order (η, δ + γ) . With the aid of MATLAB software, it appears that the statistical convergence of order (η, δ + γ) is well defined every time when (δ + γ) > η and this convergence fails when (δ + γ) < η. Moreover, we try to set up relations between (Δv, λ)-statistical convergence of order (η, δ + γ) and strongly (Δv, p, λ)-Cesàro summability of order (η, δ + γ) and give some compelling instances to show that the converse of these relations is not valid. In addition to the above results, we also graphically exhibits that if a sequence of fuzzy numbers is bounded and statistically convergent of order (η, δ + γ) in (Δv, λ), then it need not be strongly (Δv, p, λ)-Cesàro summable of order (η, δ + γ).

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 A Tauberian Theorem for Double Cesàro Summability Method

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
Bidu Bhusan Jena ◽  
Susanta Kumar Paikray ◽  
Umakanta Misra
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
De La Vallée Poussin

We have generalized Littlewood Tauberian theorems for(C,k,r)summability of double sequences by using oscillating behavior and de la Vallée-Poussin mean. Further, the generalization of(C,r)summability from(C,k,r)summability is given as corollaries which were earlier established by the authors.

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