scholarly journals Fixed Point Methods for the Generalized Stability of Functional Equations in a Single Variable

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Liviu Cădariu ◽  
Viorel Radu
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Single Variable ◽  
Stability Of Functional Equations ◽  
Fixed Point Methods ◽  
Generalized Stability

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.

scholarly journals Solution and Hyers-Ulam-Rassias Stability of Generalized Mixed Type Additive-Quadratic Functional Equations in Fuzzy Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Azadi Kenary ◽  
H. Rezaei ◽  
Y. W. Lee ◽  
G. H. Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Mixed Type ◽  
Direct Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fixed Point Methods ◽  
Rassias Stability

By using fixed point methods and direct method, we establish the generalized Hyers-Ulam stability of the following additive-quadratic functional equationf(x+ky)+f(x−ky)=f(x+y)+f(x−y)+(2(k+1)/k)f(ky)−2(k+1)f(y)for fixed integerskwithk≠0,±1in fuzzy Banach spaces.

Solution and stability of an n-dimensional functional equation

Analysis ◽  
2019 ◽  
Vol 39 (3) ◽  
pp. 107-115 ◽  
Author(s):  
Sandra Pinelas ◽  
V. Govindan ◽  
K. Tamilvanan
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
General Solution ◽  
Functional Equations ◽  
Ulam Stability ◽  
Fixed Point Methods ◽  
Fixed Positive Integer

AbstractIn this paper, we prove the general solution and generalized Hyers–Ulam stability of n-dimensional functional equations of the form\sum_{\begin{subarray}{c}i=1\\ i\neq j\neq k\end{subarray}}^{n}f\biggl{(}-x_{i}-x_{j}-x_{k}+\sum_{% \begin{subarray}{c}l=1\\ l\neq i\neq j\neq k\end{subarray}}^{n}x_{l}\biggr{)}=\biggl{(}\frac{n^{3}-9n^{% 2}+20n-12}{6}\biggr{)}\sum_{i=1}^{n}f(x_{i}),where n is a fixed positive integer with \mathbb{N}-\{0,1,2,3,4\}, in a Banach space via direct and fixed point methods.

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.

scholarly journals Fixed Points and Generalized Hyers-Ulam Stability

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
L. Cădariu ◽  
L. Găvruţa ◽  
P. Găvruţa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Open Problem ◽  
Functional Equations ◽  
Affirmative Answer ◽  
Ulam Stability ◽  
Single Variable ◽  
Result Show

In this paper we prove a fixed-point theorem for a class of operators with suitable properties, in very general conditions. Also, we show that some recent fixed-points results in Brzdęk et al., (2011) and Brzdęk and Ciepliński (2011) can be obtained directly from our theorem. Moreover, an affirmative answer to the open problem of Brzdęk and Ciepliński (2011) is given. Several corollaries, obtained directly from our main result, show that this is a useful tool for proving properties of generalized Hyers-Ulam stability for some functional equations in a single variable.

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