• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.1
• /
• pp.49-57
• /
• 2010

It is shown that for a derivation $$f(x_1{\cdots}x_{j-1}x_jx_{j+1}{\cdots}x_k)=\sum_{j=1}^{k}x_{1}{\cdots}x_{j-1}x_{j+1}{\cdots}x_kf(x_j)$$ on a unital $C^*$-algebra $\mathcal{B}$, there exists a unique $\mathbb{C}$-linear *-derivation $D:{\mathcal{B}}{\rightarrow}{\mathcal{B}}$ near the derivation, by using the Hyers-Ulam-Rassias stability of functional equations. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

• Journal of the Chungcheong Mathematical Society
• /
• v.7 no.1
• /
• pp.165-182
• /
• 1994

The aim of this paper is to give the partial answer of Vukman's conjecture [2]. From the partial answer we also generalize a classical result of Posner. We prove the following result: Let R be a prime ring with char$(R){\neq}2,3$, and 5. Suppose there exists a nonzero derivation $D:R{\rightarrow}R$ such that the mapping $x{\longmapsto}$ [[[Dx,x],x],x] is centralizing on R. Then R is commutative. Using this result and some results of Sinclair and Johnson, we generalize Yood's noncom-mutative extension of the Singer-Wermer theorem.

• Communications of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.743-755
• /
• 2019

For every inverse semigroup S with subsemigroup E of idempotents, necessary and sufficient conditions are obtained for the weighted semigroup algebra $l^1(S,{\omega})$ and its second dual to be $l^1(E)$-module amenble. Some results for the module Arens regularity of $l^1(S,{\omega})$ (as an $l^1(E)$-module) are found. If S is either of the bicyclic inverse semigroup or the Brandt inverse semigroup, it is shown that $l^1(S,{\omega})$ is module amenable but not amenable for any weight ${\omega}$.

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.4
• /
• pp.315-327
• /
• 2022

In this paper, we investigate the transferred superstability for the p-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from the p-radical functional equations: $$f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)g(y),\;\\f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)h(y),$$ where p is an odd positive integer, λ is a positive real number, and f is a complex valued function. Furthermore, the results are extended to Banach algebras. Therefore, the obtained result will be forced to the pre-results(p=1) for this type's equations, and will serve as a sample to apply it to the extension of the other known equations.