A Fixed Point Approach to the Stability of Functional Equations on Noncommutative Spaces

2015 ◽  
Vol 72 (4) ◽  
pp. 1639-1651 ◽  
Author(s):  
Tian-Zhou Xu ◽  
Zhan-Peng Yang
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Approach ◽  
Stability Of Functional Equations ◽  
Noncommutative Spaces ◽  
The Stability

Non-Archimedean hyperstability of Cauchy–Jensen functional equations on a restricted domain

2018 ◽  
Vol 24 (2) ◽  
pp. 155-165
Author(s):  
Iz-iddine EL-Fassi
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Metric Spaces ◽  
Fixed Point Approach ◽  
Nonlinear Anal ◽  
Stability Of Functional Equations ◽  
Jensen Functional ◽  
Empty Subset ◽  
The Stability ◽  
Fixed Positive Integer

Abstract Let X be a normed space, {U\subset X\setminus\{0\}} a non-empty subset, and {(G,+)} a commutative group equipped with a complete ultrametric d that is invariant (i.e., {d(x+z,y+z)=d(x,y} ) for {x,y,z\in G} ). Under some weak natural assumptions on U and on the function {\gamma\colon U^{3}\to[0,\infty)} , we study the new generalized hyperstability results when {f\colon U\to G} satisfies the inequality d\biggl{(}\alpha f\biggl{(}\frac{x+y}{\alpha}+z\biggr{)},\alpha f(z)+f(y)+f(x)% \biggr{)}\leq\gamma(x,y,z) for all {x,y,z\in U} , where {\frac{x+y}{\alpha}+z\in U} and {\alpha\geq 2} is a fixed positive integer. The method is based on a quite recent fixed point theorem (Theorem 1 in [J. Brzdȩk and K. Ciepliński, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Anal. 74 2011, 18, 6861–6867]) (cf. [8, Theorem 1]) in some functions spaces.

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.

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 A Fixed Point Approach to the Stability of Quintic and Sextic Functional Equations in Quasi--Normed Spaces

2010 ◽  
Vol 2010 (1) ◽  
pp. 423231 ◽  
Author(s):  
TianZhou Xu ◽  
JohnMichael Rassias ◽  
MatinaJohn Rassias ◽  
WanXin Xu
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Normed Spaces ◽  
Fixed Point Approach ◽  
The Stability

scholarly journals Fixed Point Theory and the Ulam Stability

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Janusz Brzdęk ◽  
Liviu Cădariu ◽  
Krzysztof Ciepliński
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Stability Of Functional Equations ◽  
Banach’S Fixed Point Theorem ◽  
The Stability ◽  
First Time ◽  
Stability Results

The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of stability of functional equations, motivated by a problem raised by Ulam in 1940.

A Fixed Point Approach to the Stability of Quadratic Functional Equations in Modular Spaces

2017 ◽  
Vol 6 (1) ◽  
pp. 171-175
Author(s):  
Seong Sik Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Fixed Point Approach ◽  
Modular Spaces ◽  
The Stability ◽  
Positive Integers ◽  
Rassias Stability

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equation f(kx + y) + f(kx – y) = 2k2f(x) + 2f(y) for any fixed positive integers k ∈ Ζ+ in modular spaces by using fixed point method.

scholarly journals Ulam stability of functional equations in 2-Banach spaces via the fixed point method

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Krzysztof Ciepliński
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Several Variables ◽  
Stability Of Functional Equations ◽  
Special Cases ◽  
The Stability

AbstractUsing the fixed point method, we prove the Ulam stability of two general functional equations in several variables in 2-Banach spaces. As corollaries from our main results, some outcomes on the stability of a few known equations being special cases of the considered ones will be presented. In particular, we extend several recent results on the Ulam stability of functional equations in 2-Banach spaces.

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