Remark on lacunary statistical convergence of fuzzy numbers

2001 ◽  
Vol 123 (1) ◽  
pp. 85-88 ◽  
Author(s):  
Joong Sung Kwon ◽  
Hong Tae Shim
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Lacunary Statistical Convergence

ON ASYMPTOTICALLY LACUNARY σ-STATISTICAL EQUIVALENT SEQUENCES OF FUZZY NUMBERS

2009 ◽  
Vol 05 (03) ◽  
pp. 589-598 ◽  
Author(s):  
EKREM SAVAŞ
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Invariant Mean ◽  
Lacunary Statistical Convergence ◽  
Sequences Of Fuzzy Numbers ◽  
Natural Combination

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.

scholarly journals Asymptotically Lacunary Statistical Equivalent Sequences of Fuzzy Numbers - doi: 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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