scholarly journals Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

scholarly journals Nonlinear Random Stability via Fixed-Point Method

2012 ◽  
Vol 2012 ◽  
pp. 1-45 ◽  
Author(s):  
Yeol Je Cho ◽  
Shin Min Kang ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
Random Normed Spaces

We prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in various complete random normed spaces.

scholarly journals The Stability of a Quadratic Functional Equation with the Fixed Point Alternative

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Choonkil Park ◽  
Ji-Hye Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
The Stability

Lee, An and Park introduced the quadratic functional equationf(2x+y)+f(2x−y)=8f(x)+2f(y)and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.

scholarly journals Stability of a Quartic Functional Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
General Solution ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
Fixed Positive Integer

We obtain the general solution of the generalized quartic functional equationf(x+my)+f(x-my)=2(7m-9)(m-1)f(x)+2m2(m2-1)f(y)-(m-1)2f(2x)+m2{f(x+y)+f(x-y)}for a fixed positive integerm. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces.

scholarly journals Fixed Points and Stability of an Additive Functional Equation ofn-Apollonius Type inC∗-Algebras

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Fridoun Moradlou ◽  
Hamid Vaezi ◽  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Additive Functional ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Generalized Derivations ◽  
Additive Functional Equation ◽  
Algebra Homomorphisms

Using the fixed point method, we prove the generalized Hyers-Ulam stability ofC∗-algebra homomorphisms and of generalized derivations onC∗-algebras for the following functional equation of Apollonius type∑i=1nf(z−xi)=−(1/n)∑1≤i<j≤nf(xi+xj)+nf(z−(1/n2)∑i=1nxi).

scholarly journals On the Generalized Hyers–Ulam Stability of a Functional Equation and Its Consequences

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Krzysztof Ciepliński
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
The Stability

AbstractThe aim of this note is to show the generalized Hyers–Ulam stability of a functional equation in four variables. In order to do this, the fixed point method is applied. As corollaries from our main result, some outcomes on the stability of some known equations will be also derived.

scholarly journals On the Stability of an -Variables Functional Equation in Random Normed Spaces via Fixed Point Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. Ebadian ◽  
M. Eshaghi Gordji ◽  
H. Khodaei ◽  
R. Saadati ◽  
Gh. Sadeghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Integer Number ◽  
Normed Spaces ◽  
Random Normed Spaces ◽  
The Stability ◽  
Rassias Stability

At first we find the solution of the functional equation where is an integer number. Then, we obtain the generalized Hyers-Ulam-Rassias stability in random normed spaces via the fixed point method for the above functional equation.

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