• Korean Journal of Mathematics
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• 제18권3호
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• pp.311-322
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• 2010

In this paper, we prove stabilities of the reciprocal difference functional equation $$r(\frac{x+y+z}{3})-r(x+y+z)=\frac{2r(x)r(y)r(z)}{r(x)r(y)+r(y)r(z)+r(z)r(x)}$$ and the reciprocal adjoint functional equation $$r(\frac{x+y+z}{3})+r(x+y+z)=\frac{4r(x)r(y)r(z)}{r(x)r(y)+r(y)r(z)+r(z)r(x)}$$ with three variables. Stabilities of the reciprocal difference functional equation and the reciprocal adjoint functional equation in two variables was proved by K. Ravi, J. M. Rassias and B. V. Senthil Kumar. We extend their results to three variables in similar types.

• 대한수학회지
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• 제41권3호
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• pp.461-477
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• 2004

It is shown that every almost linear mapping h : A\longrightarrowB of a unital $C^{*}$ -algebra A to a unital $C^{*}$ -algebra B is a homomorphism under some condition on multiplication, and that every almost linear continuous mapping h : A\longrightarrowB of a unital $C^{*}$ -algebra A of real rank zero to a unital $C^{*}$ -algebra B is a homomorphism under some condition on multiplication. Furthermore, we are going to prove the generalized Hyers-Ulam-Rassias stability of *-homomorphisms between unital $C^{*}$ -algebras, and of C-linear *-derivations on unital $C^{*}$ -algebras./ -algebras.

• 대한수학회보
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• 제53권2호
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• pp.387-398
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• 2016

Let X be a vector space over a field K of real or complex numbers and $k{\in}{\mathbb{N}}$. We prove the superstability of the following generalized Golab-Schinzel type equation $f(x_1+{\limits\sum_{i=2}^p}x_if(x_1)^kf(x_2)^k{\cdots}f(x_{i-1})^k)={\limits\prod_{i=1}^pf(x_i),x_1,x_2,{\cdots},x_p{\in}X$, where $f:X{\rightarrow}K$ is an unknown function which is hemicontinuous at the origin.