STATISTICAL CONVERGENCE IN FUZZY $n$-NORMED SPACES

B.S Reddy,M Srinivas

doi:10.12732/ijpam.v104i1.3

B.S Reddy, M Srinivas

Open Access

https://doi.org/10.12732/ijpam.v104i1.3

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Abstract

In this paper we introduce the concept of statistical convergence of a sequence in fuzzy n-normed space and defined limit point, statistical limit point and statistical cluster point of a sequence in fuzzy n-normed space. Also we establish the relationship between limit point, statistical limit point and statistical cluster point of a sequence in fuzzy n-normed space.

Highlights

Introduction and PreliminariesThe idea of fuzzy norm on a vector space was initiated by Katsaras [15] in [1984]
Later Felbin [17] introduced the concept of fuzzy normed space in [1992] which is based on the concept of fuzzy metric given by Kaleva and Siekkala [16]
In [2003] Bag and Samanta [1] discussed some of the properties of finite dimensional fuzzy normed linear spaces

Summary

Introduction and Preliminaries

The idea of fuzzy norm on a vector space was initiated by Katsaras [15] in [1984]. Later Felbin [17] introduced the concept of fuzzy normed space in [1992] which is based on the concept of fuzzy metric given by Kaleva and Siekkala [16]. 3. Statistical Convergence and Statistically Cauchy Sequences in Fuzzy n-Normed Spaces. We define the notion of statistically convergence and statistically Cauchy sequences in fuzzy n-normed space. A number sequence {xk} is said to be statistically convergent to the number l if for each ǫ > 0, the set K(ǫ) = {k ≤ n : xk − l| ≥ ǫ} has natural density zero. In this case we write st − lim xk l. The sequence {xk} is said to be statistically Cauchy sequence with respect to the fuzzy n-norm on X if for every ǫ > 0, ∃ a number N =.

Define a sequence

Since the sequence