Lacunary statistical convergence of order β in difference sequences of fuzzy numbers

This paper presents the asymptotically lacunary σ-statistical equivalent which is a natural combination of the definition for asymptotically equivalent, invariant mean and lacunary statistical convergence of fuzzy numbers. In addition, we shall also present asymptotically lacunary σ-statistical equivalent analogs of Savas and Nuray's theorems in Ref. 8.

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Asymptotically Lacunary Statistical Equivalent Sequences of Fuzzy Numbers - doi: 10.5269/bspm.v30i2.14007

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v30i2.14007 ◽

2011 ◽

Vol 30 (2) ◽

pp. 57-62

Author(s):

Ayhan Esi ◽

Necdet Çatalbas

Keyword(s):

Statistical Convergence ◽

Fuzzy Numbers ◽

Lacunary Sequence ◽

Lacunary Statistical Convergence ◽

Sequences Of Fuzzy Numbers ◽

Natural Combination

In this article we present the following definition which is natural combination of the definition for asymptotically equivalent and lacunary statistical convergence of fuzzy numbers. Let =(k_{r}) be a lacunary sequence. The two sequnces X = (X_{k}) and Y=(Y_{k}) of fuzzy numbers are said to be asymptotically lacunary statistical equivalent to multiple L provided that for every >0lim_{r}(1/(h_{r}))|{k∈I_{r}:d(((X_{k})/(Y_{k})),L)≥}|=0.

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ON ALMOST STATISTICAL CONVERGENCE OF GENERALIZED DIFFERENCE SEQUENCES OF FUZZY NUMBERS

Mathematical Modelling and Analysis ◽

10.3846/13926292.2005.9637292 ◽

2005 ◽

Vol 10 (4) ◽

pp. 345-352 ◽

Cited By ~ 5

Author(s):

M. Et ◽

Y. Altin ◽

H. Altinok

Keyword(s):

Statistical Convergence ◽

Fuzzy Numbers ◽

Almost Convergence ◽

Difference Sequences ◽

Sequences Of Fuzzy Numbers ◽

Bounded Sequences

The purpose of this paper is to introduce the concepts of almost statistical convergence and strongly almost convergence of generalized difference sequences of fuzzy numbers. We obtain some results related to these concepts. It is also shown that almost Δr λ - statistical convergence and strongly almost Δr λ - convergence are equivalent for Δr ‐bounded sequences of fuzzy numbers. Šio straipsnio tikslas supažindinti su beveik statistinio ir stipriai beveik statistinio apibendrintu fuzzy skaičiu konvergavimo savokomis. Straipsnyje taip pat parodyta, kad beveik Δr λ ‐ statistinis konvergavimas ir stipriai beveik Δr λ - statistinis konvergavimas yra ekvivalentus Δr λ - apribotoms fuzzy skaičiu sekoms.

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Applications of deferred Cesàro statistical convergence of sequences of fuzzy numbers of order (ξ, ω)

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-211201 ◽

2021 ◽

pp. 1-10

Author(s):

Sonali Sharma ◽

Uday Pratap Singh ◽

Kuldip Raj

Keyword(s):

Statistical Convergence ◽

Fuzzy Numbers ◽

Sequence Spaces ◽

Modulus Function ◽

Matlab Software ◽

Difference Sequences ◽

Cesaro Summability ◽

Convergence Of Sequences ◽

Sequences Of Fuzzy Numbers ◽

Theoretical Results

The purpose of this article is to study deferred Cesrào statistical convergence of order (ξ, ω) associated with a modulus function involving the concept of difference sequences of fuzzy numbers. The study reveals that the statistical convergence of these newly formed sequence spaces behave well for ξ ≤ ω and convergence is not possible for ξ > ω. We also define p-deferred Cesàro summability and establish several interesting results. In addition, we provide some examples which explain the validity of the theoretical results and the effectiveness of constructed sequence spaces. Finally, with the help of MATLAB software, we examine that if the sequence of fuzzy numbers is bounded and deferred Cesàro statistical convergent of order (ξ, ω) in (Δ, F, f), then it need not be strongly p-deferred Cesàro summable of order (ξ, ω) in general for 0 < ξ ≤ ω ≤ 1.

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