scholarly journals On (λ,µ)-statistical convergence of double sequences on intuitionistic fuzzy normed spaces

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 109-120 ◽  
Author(s):  
Vijay Kumar ◽  
M. Mursaleen

In this paper, we define (?, ?)- statistical convergence and (?, ?)-statistical Cauchy double sequences on intuitionistic fuzzy normed spaces (IFNS in short), where ? = (?n ) and ? = (?m) be two non-decreasing sequences of positive real numbers such that each tending to ? and ?n+1 ? ?n + 1, ?1 = 1; ?m+1 ? ?m + 1, ?1 = 1. We display example that shows our method of convergence is more general for double sequences in intuitionistic fuzzy normed spaces.

2014 ◽  
Vol 33 (2) ◽  
pp. 59-67
Author(s):  
Pankaj Kumar ◽  
S. S. Bhatia ◽  
Vijay Kumar

In this paper, we aim to generalize the notion of statistical convergence for double sequences on probabilistic normed spaces with the help of two nondecreasing sequences of positive real numbers $\lambda=(\lambda_{n})$ and $\mu = (\mu_{n})$  such that each tending to zero, also $\lambda_{n+1}\leq \lambda_{n}+1, \lambda_{1}=1,$ and $\mu_{n+1}\leq \mu_{n}+1, \mu_{1}=1.$ We also define generalized statistically Cauchy double sequences on PN space and establish the Cauchy convergence criteria in these spaces.


Author(s):  
Ömer Kişi

In this paper, we introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between I₂-statistical convergence in the corresponding intuitionistic fuzzy normed space.


2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Vatan Karakaya ◽  
Necip Şimşek ◽  
Müzeyyen Ertürk ◽  
Faik Gürsoy

We studyλ-statistically convergent sequences of functions in intuitionistic fuzzy normed spaces. We define concept ofλ-statistical pointwise convergence andλ-statistical uniform convergence in intuitionistic fuzzy normed spaces and we give some basic properties of these concepts.


2018 ◽  
Vol 24 (3) ◽  
pp. 64-78
Author(s):  
S. Melliani ◽  
◽  
M. Küçükaslan ◽  
H. Sadiki ◽  
L. S. Chadli ◽  
...  

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 811-820 ◽  
Author(s):  
Bipan Hazarika ◽  
Vijay Kumar ◽  
Bernardo Lafuerza-Guilién

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In [19], Kostyrko et al. introduced the concept of ideal convergence as a sequence (xk) of real numbers is said to be I-convergent to a real number e, if for each ? > 0 the set {k ? N : |xk - e| ? ?} belongs to I. The aim of this paper is to introduce and study the notion of ?-ideal convergence in intuitionistic fuzzy normed spaces as a variant of the notion of ideal convergence. Also I? -limit points and I?-cluster points have been defined and the relation between them has been established. Furthermore, Cauchy and I?-Cauchy sequences are introduced and studied. .


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