scholarly journals The Intuitionistic Fuzzy Normed Space of Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
B. T. Bilalov ◽  
S. M. Farahani ◽  
F. A. Guliyeva
Keyword(s):  
Banach Space ◽  
Normed Space ◽  
Canonical System ◽  
Fuzzy Normed Space ◽  
Strong Completeness ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Fuzzy Space ◽  
Fuzzy Banach Space

Intuitionistic fuzzy normed space is defined using concepts oft-norm andt-conorm. The concepts of fuzzy completeness, fuzzy minimality, fuzzy biorthogonality, fuzzy basicity, and fuzzy space of coefficients are introduced. Strong completeness of fuzzy space of coefficients with regard to fuzzy norm and strong basicity of canonical system in this space are proved. Strong basicity criterion in fuzzy Banach space is presented in terms of coefficient operator.

Intuitionistic Fuzzy 2-Metric Space and Some Topological Properties

2013 ◽  
pp. 245-260
Author(s):  
Q.M. Danish Lohani
Keyword(s):  
Metric Space ◽  
Normed Space ◽  
Fuzzy Metric Space ◽  
Topological Properties ◽  
Fuzzy Normed Space ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Norm Space

The notion of intuitionistic fuzzy metric space was introduced by Park (2004) and the concept of intuitionistic fuzzy normed space by Saadati and Park (2006). Recently Mursaleen and Lohani introduced the concept of intuitionistic fuzzy 2-metric space (2009) and intuitionistic fuzzy 2-norm space. This paper studies precompactness and metrizability in this new setup of intuitionistic fuzzy 2-metric space.

scholarly journals n-Tuplet Coincidence Point Theorems in Intuitionistic Fuzzy Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Müzeyyen Ertürk ◽  
Vatan Karakaya
Keyword(s):  
Fixed Point ◽  
Normed Space ◽  
Coincidence Point ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Coincidence Points ◽  
Tripled Fixed Point ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Intuitionistic Fuzzy Normed Spaces

For an arbitrarynpositive integer, we investigate the existence ofn-tuplet coincidence points in intuitionistic fuzzy normed space. Results of the paper are more general than those of the coupled and the tripled fixed point works in intuitionistic fuzzy normed space.

scholarly journals Schauder Basis, Separability, and Approximation Property in Intuitionistic Fuzzy Normed Space

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
M. Mursaleen ◽  
V. Karakaya ◽  
S. A. Mohiuddine
Keyword(s):  
Normed Space ◽  
Approximation Property ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Intuitionistic Fuzzy Normed Spaces

We define and study the concepts of Schauder basis, separability, and approximation property in intuitionistic fuzzy normed spaces and establish some results related to these concepts. We also display here some interesting examples by using classical sequence spaces .

scholarly journals Stability of Various Functional Equations in Non-Archimedean Intuitionistic Fuzzy Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Syed Abdul Mohiuddine ◽  
Abdullah Alotaibi ◽  
Mustafa Obaid
Keyword(s):  
Normed Space ◽  
Functional Equations ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
The Stability ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Stability Results

We define and study the concept of non-Archimedean intuitionistic fuzzy normed space by using the idea oft-norm andt-conorm. Furthermore, by using the non-Archimedean intuitionistic fuzzy normed space, we investigate the stability of various functional equations. That is, we determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framework of non-Archimedean IFN spaces.

scholarly journals ON GENERALIZED STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES

2021 ◽  
pp. 435
Author(s):  
Ömer Kişi
Keyword(s):  
Normed Space ◽  
Statistical Convergence ◽  
Double Sequences ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
New Methods ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Lacunary Statistical Convergence ◽  
Intuitionistic Fuzzy Normed Spaces

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.

scholarly journals on ideal convergence of triple sequences in intuitionistic Fuzzy normed space defined by compact operator

2021 ◽  
Vol 40 (5) ◽  
pp. 1227-1247
Author(s):  
Vakeel A. Khan ◽  
Mohd. Imran Idrisi ◽  
Umme Tuba
Keyword(s):  
Compact Operator ◽  
Normed Space ◽  
Fuzzy Topology ◽  
Fuzzy Normed Space ◽  
Ideal Convergence ◽  
Fundamental Properties ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Inclusion Relations

The main purpose of this article is to introduce and study some new spaces of I-convergence of triple sequences in intuitionistic fuzzy normed space defined by compact operator i.e 3SI (μ,ν)(T ) and 3SI0(μ,ν)(T ) and examine some fundamental properties, fuzzy topology and verify inclusion relations lying under these spaces.

scholarly journals On (λ,μ)- Zweier ideal convergence in intuitionistic fuzzy normed space

2020 ◽  
Vol 30 (4) ◽  
pp. 413-427
Author(s):  
Vakeel Khan ◽  
Mobeen Ahmad
Keyword(s):  
Normed Space ◽  
Double Sequences ◽  
Real Numbers ◽  
Fuzzy Normed Space ◽  
Positive Real ◽  
Ideal Convergence ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Cauchy Sequences ◽  
New Type

In this paper, we study and introduce a new type of convergence, namely (?,?)- Zweier convergence and (?,?)- Zweier ideal convergence of double sequences x = (xij) in intuitionistic fuzzy normed space (IFNS), where ? = (?n) and ?= (?m) are two non-decreasing sequences of positive real numbers such that each tending to infinity. Furthermore, we studied (?,?)- Zweier Cauchy and (?,?)- Zweier ideal Cauchy sequences on the said space and established a relation between them.

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