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Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in multi-Banach algebras and derivations on multi-Banach algebras for the additive functional equation $\sum_{i = 1}^{m} f (m x_{i} + \sum_{j = 1, j \neq i}^{m} x_{j}) + f (\sum_{i = 1}^{m} x_{i}) = 2 f (\sum_{i = 1}^{m} m x_{i})$ for each $m \in ℕ$ with $m \geq 2$ .

Some fixed point theorems in logarithmic convex structures

Alireza Moazzen; Yoel-Je Cho; Choonkil Park; Madjid Eshaghi Gordji — 2017

Mathematica Bohemica

Generalized stability of $C^{*}$ -ternary quadratic mappings.

Park, Choonkil; Cui, Jianlian — 2007

Abstract and Applied Analysis

Homomorphisms and derivations in $C^{*}$ -algebras.

Park, Choonkil; Najati, Abbas — 2007

Abstract and Applied Analysis

Stability of a generalized Euler-Lagrange type additive mapping and homomorphisms in $C^{*}$ -algebras.

Najati, Abbas; Park, Choonkil — 2009

Advances in Difference Equations [electronic only]

Stability of a generalized Euler-Lagrange type additive mapping and homomorphisms in $C^{*}$ -algebras.

Najati, Abbas; Park, Choonkil — 2010

The Journal of Nonlinear Sciences and its Applications

Stability of homomorphisms and generalized derivations on Banach algebras.

Najati, Abbas; Park, Choonkil — 2009

Journal of Inequalities and Applications [electronic only]

Fixed points and stability of a generalized quadratic functional equation.

Najati, Abbas; Park, Choonkil — 2009

Journal of Inequalities and Applications [electronic only]

Inequalities in additive $N$ -isometries on linear $N$ -normed Banach spaces.

Park, Choonkil; Rassias, Themistocles M. — 2007

Journal of Inequalities and Applications [electronic only]

Stability of the Cauchy-Jensen functional equation in $C^{*}$ -algebras: a fixed point approach.

Park, Choonkil; An, Jong Su — 2008

Fixed Point Theory and Applications [electronic only]

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Fixed points and stability of the Cauchy functional equation in $C^{*}$ -algebras.

A fixed point approach to the fuzzy stability of an additive-quadratic-cubic functional equation.

Fuzzy stability of additive functional inequalities with the fixed point alternative.

Fuzzy stability of an additive-quadratic-quartic functional equation.

Fixed points and the stability of an AQCQ-functional equation in non-Archimedean normed spaces.

Fixed points, inner product spaces, and functional equations.

Fixed points and Hyers--Ulam--Rassias stability of Cauchy--Jensen functional equations in Banach algebras.

Generalized Hyers-Ulam stability of quadratic functional equations: a fixed point approach.

On the Cauchy functional inequality in Banach modules.

Fixed points in functional inequalities.

Approximate homomorphisms and derivation in multi-Banach algebras

Some fixed point theorems in logarithmic convex structures

Generalized stability of $C^{*}$ -ternary quadratic mappings.

Homomorphisms and derivations in $C^{*}$ -algebras.

Stability of a generalized Euler-Lagrange type additive mapping and homomorphisms in $C^{*}$ -algebras.

Stability of a generalized Euler-Lagrange type additive mapping and homomorphisms in $C^{*}$ -algebras.

Stability of homomorphisms and generalized derivations on Banach algebras.

Fixed points and stability of a generalized quadratic functional equation.

Inequalities in additive $N$ -isometries on linear $N$ -normed Banach spaces.

Stability of the Cauchy-Jensen functional equation in $C^{*}$ -algebras: a fixed point approach.