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 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 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.

A FIXED POINT APPROACH TO THE STABILITY OF GENERAL QUADRATIC EULER-LAGRANGE FUNCTIONAL EQUATIONS IN INTUITIONISTIC FUZZY SPACES

2016 ◽  
pp. 4430-4436
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Fixed Point Approach ◽  
Intuitionistic Fuzzy ◽  
The Stability ◽  
Lagrange Functional ◽  
Intuitionistic Fuzzy Normed Spaces

In this paper, we prove the generalized Hyers-Ulam stability of a general k-quadratic Euler-Lagrange functional equation:for any fixed positive integer in intuitionistic fuzzy normed spaces using a fixed point method.

scholarly journals Nonlinear L-fuzzy stability of k-cubic functional equation

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1137-1148 ◽  
Author(s):  
Reza Saadati ◽  
Yeol Cho ◽  
John Rassias
Keyword(s):  
Functional Equation ◽  
Set Theory ◽  
Normed Space ◽  
Lattice Theory ◽  
Functional Equations ◽  
Stability Result ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Cubic Functional Equation ◽  
The Stability

In this paper, we establish the stability result for the k-cubic functional equation 2[kf (x+ky)+f (kx-y)]=k(k2+1)[f(x+y)+f(x-y)] + 2(k4-1) f(y), where k is a real number different from 0 and 1, in the setting of various L-fuzzy normed spaces that in turn generalize a Hyers-Ulam stability result in the framework of classical normed spaces. First we shall prove the stability of k-cubic functional equations in the L-fuzzy normed space under arbitrary t-norm which generalizes previous works. Then we prove the stability of k-cubic functional equations in the non- Archimedean L-fuzzy normed space. We therefore provide a link among different disciplines: fuzzy set theory, lattice theory, non-Archimedean spaces and mathematical analysis.

scholarly journals Intuitionistic Fuzzy Stability of Functional Equations Associated with Inner Product Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Zhihua Wang ◽  
Themistocles M. Rassias
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Inner Product ◽  
Product Spaces ◽  
Normed Spaces ◽  
Inner Product Spaces ◽  
Intuitionistic Fuzzy ◽  
Stability Of Functional Equations ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Stability Results

In intuitionistic fuzzy normed spaces, we investigate some stability results for the functional equation which is said to be a functional equation associated with inner products space.

scholarly journals Intuitionistic fuzzy stability of Jensen-type quadratic functional equations

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 663-676 ◽  
Author(s):  
Zhihua Wang ◽  
Themistocles Rassias ◽  
Reza Saadati
Keyword(s):  
Real Number ◽  
Functional Equations ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Intuitionistic Fuzzy ◽  
Nonzero Real Number ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Stability Results

In this paper, we prove some stability results for Jensen-type quadratic functional equations 2f (x+y/2)+ 2f (x-y/2) = f (x) + f (y), f (ax+ay) + f (ax-ay) = 2a2f(x) + 2a2 f(y) in intuitionistic fuzzy normed spaces for a nonzero real number a with a ? ?1/2

scholarly journals On the probabilistic stability of some functional equations

2013 ◽  
Vol 29 (1) ◽  
pp. 125-132
Author(s):  
CLAUDIA ZAHARIA ◽  
◽  
DOREL MIHET ◽  
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Of Functional Equations ◽  
The Stability ◽  
Stability Results

We establish stability results concerning the additive and quadratic functional equations in complete Menger ϕ-normed spaces by using fixed point theory. As particular cases, some theorems regarding the stability of functional equations in β - normed and quasi-normed spaces are obtained.

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.

On the stability of some functional equations in Menger φ-normed spaces

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Dorel Miheţ ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
The Stability ◽  
Stability Results

AbstractRecently, the authors [MIHEŢ, D.—SAADATI, R.—VAEZPOUR, S. M.: The stability of an additive functional equation in Menger probabilistic φ-normed spaces, Math. Slovaca 61 (2011), 817–826] considered the stability of an additive functional in Menger φ-normed spaces. In this paper, we establish some stability results concerning the cubic, quadratic and quartic functional equations in complete Menger φ-normed spaces via fixed point theory.

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