Hyers–Ulam–Rassias Stability of a Quadratic and Additive Functional Equation in Quasi-Banach Spaces

2009 ◽  
Vol 6 (2) ◽  
pp. 233-248 ◽  
Author(s):  
Fridoun Moradlou ◽  
Hamid Vaezi ◽  
G. Zamani Eskandani
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Additive Functional ◽  
Additive Functional Equation ◽  
Rassias Stability

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 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 Hyers-Ulam stability of a finite variable mixed type quadratic-additive functional equation in quasi-Banach spaces

2020 ◽  
Vol 5 (6) ◽  
pp. 5993-6005 ◽  
Author(s):  
K. Tamilvanan ◽  
◽  
Jung Rye Lee ◽  
Choonkil Park ◽  
◽  
...  
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Mixed Type ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation

scholarly journals Hyers–Ulam Stability of Additive Functional Equation Using Direct and Fixed-Point Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
K. Tamilvanan ◽  
G. Balasubramanian ◽  
Nazek Alessa ◽  
K. Loganathan
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonnegative Integer ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Fixed Point Methods ◽  
Stability Results

In this present work, we obtain the solution of the generalized additive functional equation and also establish Hyers–Ulam stability results by using alternative fixed point for a generalized additive functional equation χ ∑ g = 1 l v g = ∑ 1 ≤ g < h < i ≤ l χ v g + v h + v i − ∑ 1 ≤ g < h ≤ l χ v g + v h − l 2 − 5 l + 2 / 2 ∑ g = 1 l χ v g − χ − v g / 2 . where l is a nonnegative integer with ℕ − 0,1,2,3,4 in Banach spaces.

Approximate $n$-dimensional additive functional equation in various Banach spaces

2018 ◽  
Vol 11 (2) ◽  
pp. 77-96
Author(s):  
Abasalt Bodaghi ◽  
Mohan Arunkumar ◽  
Elumalai Sathya
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Additive Functional ◽  
Additive Functional Equation

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).

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