• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.933-944
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• 2013

Based on the four kinds of theoretical definitions of the continuous module homomorphism between random locally convex modules, we first show that among them there are only two essentially. Further, we prove that such two are identical if the family of $L^0$-seminorms for the former random locally convex module has the countable concatenation property, meantime we also provide a counterexample which shows that it is necessary to require the countable concatenation property.

• Korean Journal of Mathematics
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• v.19 no.1
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• pp.87-99
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• 2011

Using the Hyers-Ulam-Rassias stability method of functional equations, we investigate homomorphisms in proper $CQ^*$-algebras and proper Lie $CQ^*$-algebras, and derivations on proper $CQ^*$-algebras and proper Lie $CQ^*$-algebras associated with the following functional equation $$\frac{1}{k}f(kx+ky+kz)=f(x)+f(y)+f(z)$$ for a fixed positive integer $k$.

• Korean Journal of Mathematics
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• v.19 no.1
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• pp.33-52
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• 2011

We prove the Hyers-Ulam stability of partitioned functional equations in Banach modules over a unital $C^*$-algebra. It is applied to show the stability of algebra homomorphisms in Banach algebras associated with partitioned functional equations in Banach algebras.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.401-410
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• 2002

We prove the generalized Hyers-Ulam-Rassias stability of generalized Jensen's functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with generalized Jensen's functional equations in Banach algebras.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.467-474
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• 2004

We prove the generalized Hyers-Ulam-Rassias stability of a partitioned functional equation. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with partitioned functional equations in Banach algebras.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.195-209
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• 2010

In this paper, we prove the generalized Hyers-Ulam stability of bi-homomorphisms in $C^*$-ternary algebras and of bi-derivations on $C^*$-ternary algebras for the following bi-additive functional equation f(x + y, z - w) + f(x - y, z + w) = 2f(x, z) - 2f(y, w). This is applied to investigate bi-isomorphisms between $C^*$-ternary algebras.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.245-261
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• 2006

In this paper, we prove the generalized Hyers-Ulam stability of ring homomorphisms over the p-adic field $\mathbb{Q}_p$ associated with the Cauchy functional equation f(x+y) = f(x)+f(y) and the Cauchy-Jensen functional equation $2f(\frac{x+y}{2}+z)=f(x)+f(y)+2f(z)$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.147-162
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• 2011

In this paper, we investigate the Ulam-Hyers stability of $C^{\star}$-ternary algebra 3-homomorphisms for the functional equation $$f(x_1+x_2,y_1+y_2,z_1+z_2)=\;\displaystyle\sum_{1{\leq}i,j,k{\leq}2}\;f(x_i,y_j,z_k)$$ in $C^{\star}$-ternary algebras.

• Journal of the Korean Mathematical Society
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• v.19 no.2
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• pp.117-122
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• 1983

• Communications of the Korean Mathematical Society
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• v.2 no.2
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• pp.251-258
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• 1987