fuzzy banach space
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2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Safoura Rezaei Aderyani ◽  
Reza Saadati

AbstractIn this article, first, we present an example of fuzzy normed space by means of the Mittag-Leffler function. Next, we extend the concept of fuzzy normed space to matrix valued fuzzy normed space and also we introduce a class of matrix valued fuzzy control functions to stabilize a nonlinear ϕ-Hadamard fractional Volterra integro-differential equation. In this sense, we investigate the Ulam–Hyers–Rassias stability for this kind of fractional equations in matrix valued fuzzy Banach space. Finally, as an application, we investigate the Ulam–Hyers–Rassias stability using matrix valued fuzzy control function obtained through the Mittag-Leffler function.


2016 ◽  
Vol 09 (12) ◽  
pp. 5970-5979 ◽  
Author(s):  
Gang Lu ◽  
Jun Xie ◽  
Qi Liu ◽  
Yuanfeng Jin

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1067-1080
Author(s):  
Zhihua Wang ◽  
Prasanna Sahoo

Using the fixed point method, we prove some results concerning the stability of the functional equation 2n?i=1 f(xi-1/2n 2n?j=1 xj)=2n?i=1 f (xi)-2nf(1/2n 2n?i=1 xi) where f is defined on a vector space and taking values in a fuzzy Banach space, which is said to be a functional equation related to a characterization of inner product spaces.


Organizacija ◽  
2014 ◽  
Vol 47 (2) ◽  
pp. 90-97 ◽  
Author(s):  
Farnaz Solatikia ◽  
Erdem Kiliç ◽  
Gerhard Wilhelm Weber

Abstract Background: This paper generalizes the results of Embedding problem of Fuzzy Number Space and its extension into a Fuzzy Banach Space C(Ω) × C(Ω), where C(Ω) is the set of all real-valued continuous functions on an open set Ω. Objectives: The main idea behind our approach consists of taking advantage of interplays between fuzzy normed spaces and normed spaces in a way to get an equivalent stochastic program. This helps avoiding pitfalls due to severe oversimplification of the reality. Method: The embedding theorem shows that the set of all fuzzy numbers can be embedded into a Fuzzy Banach space. Inspired by this embedding theorem, we propose a solution concept of fuzzy optimization problem which is obtained by applying the embedding function to the original fuzzy optimization problem. Results: The proposed method is used to extend the classical Mean-Variance portfolio selection model into Mean Variance-Skewness model in fuzzy environment under the criteria on short and long term returns, liquidity and dividends. Conclusion: A fuzzy optimization problem can be transformed into a multiobjective optimization problem which can be solved by using interactive fuzzy decision making procedure. Investor preferences determine the optimal multiobjective solution according to alternative scenarios.


2013 ◽  
Vol 373-375 ◽  
pp. 1881-1884
Author(s):  
Xiao Jing Zhan ◽  
Pei Sheng Ji

In this paper, we investigate the Hyers-Ulam stability of the functional equation ƒ(2x+y)+ƒ(2x-y)=8ƒ(x)+2ƒ(y) in fuzzy Banach space using the fixed point method.


2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
G. Zamani Eskandani ◽  
P. Găvruţa ◽  
Gwang Hui Kim

We investigate the generalized Ulam-Hyers stability of the Cauchy functional equation and pose two open problems in fuzzy Banach space.


2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
B. T. Bilalov ◽  
S. M. Farahani ◽  
F. A. Guliyeva

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.


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