scholarly journals On the Cauchy–Rassias stability of a generalized additive functional equation

2008 ◽  
Vol 339 (1) ◽  
pp. 372-383 ◽  
Author(s):  
Jung-Rye Lee ◽  
Dong-Yun Shin
Keyword(s):  
Functional Equation ◽  
Additive Functional ◽  
Additive Functional Equation ◽  
Rassias Stability

scholarly journals Solutions and the Generalized Hyers-Ulam-Rassias Stability of a Generalized Quadratic-Additive Functional Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Janfada ◽  
R. Shourvazi
Keyword(s):  
Functional Equation ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
General Solutions ◽  
Rassias Stability

We study general solutions and generalized Hyers-Ulam-Rassias stability of the following -dimensional functional equation , , on non-Archimedean normed spaces.

scholarly journals Stability of n-Dimensional Additive Functional Equation in Generalized 2-Normed Space

2016 ◽  
Vol 49 (3) ◽  
Author(s):  
M. Arunkumar
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Normed Space ◽  
Additive Functional ◽  
Additive Functional Equation ◽  
Rassias Stability

AbstractIn this paper, the author established the general solution and generalized Ulam-Hyers-Rassias stability of n-dimensional additive functional equationin generalized 2-normed space.

scholarly journals Homomorphisms and Derivations inC*-Algebras

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Choonkil Park ◽  
Abbas Najati
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Additive Functional ◽  
Additive Functional Equation ◽  
Stability Method ◽  
Rassias Stability

Using the Hyers-Ulam-Rassias stability method of functional equations, we investigate homomorphisms inC*-algebras, LieC*-algebras, andJC*-algebras, and derivations onC*-algebras, LieC*-algebras, andJC*-algebras associated with the following Apollonius-type additive functional equationf(z−x)+f(z−y)+(1/2)f(x+y)=2f(z−(x+y)/4).

scholarly journals Functional Inequalities Associated with Cauchy Additive Functional Equation in Non-Archimedean Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
A. Ebadian ◽  
N. Ghobadipour ◽  
Th. M. Rassias ◽  
M. Eshaghi Gordji
Keyword(s):  
Functional Equation ◽  
Additive Functional ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Rassias Stability

We investigate the generalized Hyers-Ulam stability of the functional inequalities∥f((x+y+z)/4)+f((3x−y−4z)/4)+f((4x+3z)/4)∥≤∥2f(x)∥and∥f((y−x)/3)+f((x−3z)/3)+f((3x+3z−y)/3)∥≤∥f(x)∥in non-Archimedean normed spaces in the spirit of the Th. M. Rassias stability approach.

scholarly journals Fuzzy approximation of an additive functional equation

2011 ◽  
Vol 9 (2) ◽  
pp. 205-215 ◽  
Author(s):  
G. Zamani Eskandani ◽  
Ali Reza Zamani ◽  
H. Vaezi
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Banach Spaces ◽  
Normed Space ◽  
Additive Functional ◽  
Additive Functional Equation ◽  
Fuzzy Approximation ◽  
The Stability ◽  
Rassias Stability

In this paper, we investigate the generalized Hyers– Ulam– Rassias stability of the functional equation∑i=1mf(mxi+∑j=1, j≠imxj)+f(∑i=1mxi)=2f(∑i=1mmxi)in fuzzy Banach spaces and some applications of our results in the stability of above mapping from a normed space to a Banach space will be exhibited.

scholarly journals Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias Stabilities of an Additive Functional Equation in Several Variables

2007 ◽  
Vol 2007 ◽  
pp. 1-6 ◽  
Author(s):  
Paisan Nakmahachalasint
Keyword(s):  
Functional Equation ◽  
Additive Functional ◽  
Additive Functional Equation ◽  
Several Variables ◽  
Rassias Stability

It is well known that the concept of Hyers-Ulam-Rassias stability was originated by Th. M. Rassias (1978) and the concept of Ulam-Gavruta-Rassias stability was originated by J. M. Rassias (1982–1989) and by P. Găvruta (1999). In this paper, we give results concerning these two stabilities.

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