• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.197-208
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• 2008

In this paper, we obtain the Hyers-Ulam-Rassias stability of a Cauchy-Jensen functional equation $$f(x+y,z)-f(x,z)-f(y,z)=0,\\2f(x,\frac{y+z}2)-f(x,y)-f(x,z)=0$$ in the spirit of Th. M. Rassias.

• The Pure and Applied Mathematics
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• v.16 no.2
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• pp.167-178
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• 2009

In this paper, we obtain the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation f(x+y, z)-f(x, z)-f(y, z)=0, $$2f\;x,\;{\frac{y+z}{2}}-f(x,\;y)-f(x,\;z)=0$$ in the spirit of P. $G{\breve{a}}vruta$.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.153-161
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• 2008

In the present paper we introduce a Jensen type quartic functional equation and then investigate the generalized Hyers-Ulam stability problem for the equation.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.57-73
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• 2005

In this paper we solve a generalized quadratic Jensen type functional equation $m^2 f (\frac{x+y+z}{m}) + f(x) + f(y) + f(z) =n^2 [f(\frac{x+y}{n}) +f(\frac{y+z}{n}) +f(\frac{z+x}{n})]$ and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.133-142
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• 2008

Given an $m{\in}\mathbb{N}$ and two vector spaces V and W, a function f : $V^m{\rightarrow}W$ is called multi-Jensen if it satisfies Jensen's equation in each variable separately. In this paper we unify these m Jensen equations to obtain a single functional equation for f and prove its stability in the sense of Hyers-Ulam, using the so-called direct method.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.15-19
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• 2001

We prove the Hyers-Ulam-Rassias stability of the Jensen's equation in left Banach B-modules over a unital Banach algebra B.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.31-37
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• 2009

In this paper, we obtain the generalized Hyers-Ulam stability of a functional equation and a system of functional equations on Jensen-quadratic mappings.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.173-182
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• 2007

In this paper, we prove the Cauchy-Rassias stability of derivations on quasi-Banach algebras associated to the Cauchy functional equation and the Jensen functional equation. We use the Cauchy-Rassias inequality that was first introduced by Th. M. Rassias in the paper "On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300".

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.513-519
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• 2007

In this paper, we obtain the general solution and the stability of the multi-dimensional Jensen's functional equation $$2f(\frac{x_1+y_1}{2},\;\cdots,\;\frac{x_n+y_n}{2})=f(x_1,\;\cdots,\;x_n)+f(y_1,\;\cdots,\;y_n)$$. The function f given by $f(x_1,\;\cdots,\;x_n)=a_1x_1+{\cdots}+a_nx_n+b$ is a solution of the above functional equation.

• 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.