• 충청수학회지
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• 제15권1호
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• pp.35-41
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• 2002

In this paper, we prove the stability of a Jensen's functional equation on a normed almost linear space.

• 충청수학회지
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• 제14권1호
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• pp.113-122
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• 2001

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

• 충청수학회지
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• 제14권1호
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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.

• 대한수학회보
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• 제45권1호
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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.

• 대한수학회보
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• 제46권4호
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• pp.645-656
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• 2009

J. Wang [21] proposed a problem: whether the Hyers-Ulam-Rassias stability of Jensen's equation for the case p, q, r, s $\in$ ($\beta$, $\frac{1}{\beta}$) \ {1} holds or not under the assumption that G and E are $\beta$-homogeneous Fspace (0 < $\beta\;\leq$ 1). The main purpose of this paper is to give an answer to Wang's problem. Furthermore, we proved that the stability property of Jensen's equation is not true as long as p or q is equal to $\beta$, $\frac{1}{\beta}$, or $\frac{\beta_2}{\beta_1}$ (0 < $\beta_1,\beta_2\leq$ 1).

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.423-430
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• 2003

We prove the generalized Hyers-Ulam-Rhssias stability of the Jensen's equation in Banach modules over a Banach algebra.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권2호
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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.

• 대한수학회보
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• 제39권3호
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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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• 제24권1_2호
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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.

• Korean Journal of Mathematics
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• 제15권2호
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• pp.135-148
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• 2007

We prove the stability of generalized Jensen's equations in a Hilbert module over a unital $C^*$-algebra. This is applied to show the stability of a projection, a unitary operator, a self-adjoint operator, a normal operator, and an invertible operator in a Hilbert module over a unital $C^*$-algebra.