• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.841-849
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• 2007

In this paper we discuss the Hyers-Ulam-Rassias stability of a system of first order linear recurrences with variable coefficients in Banach spaces. The concept of the Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. As an application, the Hyers-Ulam-Rassias stability of a p-order linear recurrence with variable coefficients is proved.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.825-840
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• 2007

In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.325-336
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• 2001

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of a quadratic function equation f(x+y+z)+f(x-y)+f(y-z)+f(z-x)=3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam-Rassias stability of the equation on bounded domain.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.437-446
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• 1997

In this paper, the Hyers-Ulam stability and the general Hyers-Ulam stability (more precisely, modified Hyers-Ulam-Rassias stability) of the gamma functional equation (3) in the following setings $$ \left$\mid$ f(x + 1) - xf(x) \right$\mid$ \leq \delta and \left$\mid$ \frac{xf(x)}{f(x + 1)} - 1 \right$\mid$ \leq \frac{x^{1+\varepsilon}{\delta} $$ shall be proved.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.607-619
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• 2001

Rassias obtained the Hyers-Ulam stability of the gen-eral Euler-Lagrange functional equation. In this paper we general-ized this stability in the spirit of Hyers, Ulam, Rassias and Gavruta.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.117-137
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• 2007

We establish the Hyers-Ulam-Rassias stability of the Pexiderized mixed type quadratic equation $f_1(x+y+z)+f_2(x-y)+f_3(x-z)-f_4(x-y-z)-f_5(x+y)-f_6(x+z)=0$ in the spirit of D. H. Hyers, S. M. Ulam and Th. M. Rassias.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.321-338
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• 2005

In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(X))\;=\;\phi(X)f(X)$, where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers, Ulam, Rassias, and Gavruta for many other equations such as the gamma, beta, Schroder, iterative, and G-function type's equations.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.1-14
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• 2008

In this paper, we prove the Hyers-Ulam-Rassias stability of the Cauchy functional equation f(x+y) = f(x)+f(y) and of the Jensen functional equation $2f(\frac{x+y}{2})=f(x)+f(y)$ over the p-adic field ${\mathbb{Q}}_p$. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.211-223
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• 2001

In this paper, we obtain the modified Hyers-Ulam-Rassias stability for the family of the functional equation f(x o y) = H(f(x)(sup)1/t, f(y)(sup)1/t)(x,y) $\in$S), where H is a s homogeneous function of degree t and o is a square-symmetric operation on the set S.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.111-124
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• 2000

In this paper we obtain the Hyers-Ulam-Rassias stability of the Pexider equation f(x+y) =g(x)+h(y) in the spirit of Hyers, Ulam, Rassias and Gavruta.