• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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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.

• 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.

• 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.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.

• 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.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.

• The Pure and Applied Mathematics
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• v.18 no.2
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• pp.161-172
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• 2011

In this paper we investigate the Hyers-Ulam stability of a Jensen type functional equation in multi-normed spaces and then extend the result to multi-normed left modules over a normed algebra A.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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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).

• The Pure and Applied Mathematics
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• v.18 no.2
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• pp.113-128
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• 2011

Let f : ${\mathbb{R}}{\rightarrow}{\mathbb{C}}$. We consider the Hyers-Ulam stability of Jensen type functional inequality $$|f(px+qy)-Pf(x)-Qf(y)|{\leq}{\epsilon}$$ in the half planes {(x, y) : $kx+sy{\geq}d$} for fixed d, k, $s{\in}{\mathbb{R}}$ with $k{\neq}0$ or $s{\neq}0$. As consequences of the results we obtain the asymptotic behaviors of f satisfying $$|f(px+qy)-Pf(x)-Qf(y)|{\rightarrow}0$$ as $kx+sy{\rightarrow}{\infty}$.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.53-61
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• 2003

We prove the generalized Hyers-Ulam-Rassias stability of the invertible mapping in a Banach module over a unital Banach algebra, and prove the generalized Hyers-Ulam-Rassias stability of the Jensen's functional equations in a Hilbert module over a unital $C^{*}$-algebra.