STABILITY OF J*-DERIVATIONS

2012 ◽  
Vol 09 (05) ◽  
pp. 1220009
Author(s):  
CHOONKIL PARK ◽  
JUNG RYE LEE ◽  
DONG YUN SHIN
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Direct Method ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability

Gordji et al. proved the Hyers–Ulam stability and the superstability of J*-derivations in J*-algebras for the generalized Jensen type functional equation [Formula: see text] by using direct method and by fixed point method. They only proved the theorems for the case r > 1. In this paper, we prove the Hyers–Ulam stability and the superstability of J*-derivations in J*-algebras for the case r ≠ 0 of the above generalized Jensen type functional equation by using direct method and by fixed point method under slightly different conditions.

scholarly journals On a functional equation that has the quadratic-multiplicative property

2020 ◽  
Vol 18 (1) ◽  
pp. 837-845 ◽  
Author(s):  
Choonkil Park ◽  
Kandhasamy Tamilvanan ◽  
Ganapathy Balasubramanian ◽  
Batool Noori ◽  
Abbas Najati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Direct Method ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Multiplicative Property ◽  
Multiplicative Functional

Abstract In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation: \phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v)] by using the direct method and the fixed point method.

scholarly journals The cubic ρ-functional equation in matrix non-Archimedean random normed spaces

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2643-2653
Author(s):  
Zhihua Wang ◽  
Chaozhu Hu
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Real Number ◽  
Direct Method ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Cubic Functional Equation ◽  
Random Normed Spaces

Using the direct method and fixed point method, we investigate the Hyers-Ulam stability of the following cubic ?-functional equation f(x+2y) + f(x-2y)- 2f(x+y)-2f(x-y)-12f(x) = ?(4f(x+y/2) + 4f(x-y/2)-f(x+y)-f(x-y)-6f(x)) in matrix non-Archimedean random normed spaces, where ? is a fixed real number with ? ? 2.

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.

Stability of Quadratic Functional Equation in Fuzzy Banach Space

2013 ◽  
Vol 373-375 ◽  
pp. 1881-1884
Author(s):  
Xiao Jing Zhan ◽  
Pei Sheng Ji
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fuzzy Banach Space

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.

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 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 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 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 Stability of a General Bilinear Functional Equation

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Anna Bahyrycz ◽  
Justyna Sikorska
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Fixed Point ◽  
Linear Space ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Bilinear Functional ◽  
Complex Linear ◽  
Class Of Functions

AbstractWe prove the Hyers–Ulam stability of the functional equation $$\begin{aligned}&f(a_1x_1+a_2x_2,b_1y_1+b_2y_2)=C_{1}f(x_1,y_1)\nonumber \\ \nonumber \\&\quad +C_{2}f(x_1,y_2)+C_{3}f(x_2,y_1)+C_{4}f(x_2,y_2) \end{aligned}$$ f ( a 1 x 1 + a 2 x 2 , b 1 y 1 + b 2 y 2 ) = C 1 f ( x 1 , y 1 ) + C 2 f ( x 1 , y 2 ) + C 3 f ( x 2 , y 1 ) + C 4 f ( x 2 , y 2 ) in the class of functions from a real or complex linear space into a Banach space over the same field. We also study, using the fixed point method, the generalized stability of $$(*)$$ ( ∗ ) in the same class of functions. Our results generalize some known outcomes.

Sign in / Sign up

Export Citation Format

Share Document