• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.383-398
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• 2009

In this paper, we study the generalized Hyers-Ulam stability of a bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,w)+f(y,\;z)+f(y,w)$$. Moreover, we establish stability results on the punctured domain.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.401-411
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• 2014

In this paper, we prove the generalized Hyers-Ulam stability of the following Jensen type functional equation $$f(\frac{x-y}{n}+z)+f(\frac{y-z}{n}+x)+f(\frac{z-x}{n}+y)=f(x)+f(y)+f(z)$$ in p-Banach spaces for any fixed nonzero integer n.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.705-720
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• 2008

In this paper, we obtain the Hyers-Ulam-Rassias stability of a bi-Jensen functional equation $4f(\frac {x+y}{2},\;\frac {z+w}{2})=f(x,z)+f(x,w)+f(y,z)+f(y,w)$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.159-170
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• 2012

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

• 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.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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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.

• 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. $G{\breve{a}}vruta$.

• 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).

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.361-370
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• 2008

We consider the Hyers-Ulam type stability of the Cauchy, Jensen, Pexider, Pexider-Jensen differences: $$(0.1){\hspace{55}}C(u):=u{\circ}A-u{\circ}P_1-u{\circ}P_2,\\(0.2){\hspace{55}}J(u):=2u{\circ}\frac{A}{2}-u{\circ}P_1-u{\circ}P_2,\\(0.3){\hspace{18}}P(u,v,w):=u{\circ}A-v{\circ}P_1-w{\circ}P_2,\\(0.4)\;JP(u,v,w):=2u{\circ}\frac{A}{2}-v{\circ}P_1-w{\circ}P_2$$, with respect to bounded distributions.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.387-400
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• 2009

We establish a new strategy to study the Hyers-Ulam-Rassias stability of the Cauchy and Jensen equations in non-Archimedean normed spaces. We will also show that under some restrictions, every function which satisfies certain inequalities can be approximated by an additive mapping in non-Archimedean normed spaces. Some applications of our results will be exhibited. In particular, we will see that some results about stability and additive mappings in real normed spaces are not valid in non-Archimedean normed spaces.