• Korean Journal of Mathematics
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• 제27권1호
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• pp.81-92
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• 2019

We introduce a reciprocal-negative Fermat's equation generalized with constants coefficients and investigate its stability in a quasi-${\beta}$-normed space.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.415-426
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• 2020

In this paper, we will prove some uniqueness theorems that can be applied to the generalized Hyers-Ulam stability of some additive-quadratic-cubic functional equation in complete modular spaces without Δ₂-conditions.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.413-421
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• 2003

In this paper, using an idea from the direct method of Hyers and Ulam, we investigate the situations so that the Hyers-Ulam-Rassias stability of the functional equation $g(x^2)\;=\;2xg(x)$ is satisfied.

• 대한수학회논문집
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• 제8권2호
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• pp.289-301
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• 1993

• Korean Journal of Mathematics
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• 제23권1호
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• pp.11-27
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• 2015

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a at bottom. The main objective in this paper is to apply the generalized Riccati equation mapping method for obtaining more exact traveling wave solutions of Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation. More precisely, the obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functional form. Solutions obtained are potentially significant for the explanation of better insight of physical aspects of the considered nonlinear physical models.

• East Asian mathematical journal
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• 제32권3호
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• pp.413-423
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• 2016

In this paper, we consider the functional equation f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 3f(y) + 3f(-y) = 0 and prove the generalized Hyers-Ulam stability for it when the target space is a fuzzy Banach space. The usual method to obtain the stability for mixed type functional equation is to split the cases according to whether the involving mappings are odd or even. In this paper, we show that the stability of a quadratic-cubic mapping can be obtained without distinguishing the two cases.

• East Asian mathematical journal
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• 제34권1호
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• pp.69-84
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• 2018

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source for each independent kernels h and g with respect to Volterra terms. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.817-825
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• 2014

In this paper, we prove the generalized Hyers-Ulam stability of the following cubic funtional equation f(2x + y) + f(2x - y) = 2f(x + 2y) - 4f(x + y) + 18f(x) - 12f(y) by the direct method in 2-normed spaces.

• East Asian mathematical journal
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• 제32권1호
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• pp.117-128
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• 2016

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source $$u^{{\prime}{\prime}}-M(x,t,{\parallel}{\bigtriangledown}u(t){\parallel}^2){\bigtriangleup}u+{\int}_0^th(t-{\tau})div[a(x){\bigtriangledown}u({\tau})]d{\tau}+{\mid}u{\mid}^{\gamma}u=0$$. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.171-180
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• 2011

In this paper, we study the superstability problem bounded by two-variables of Th. M. Rassias type for the generalized sine functional equations $$g(x+y)f(x-y)=f(x)^2-f(y)^2 \\ f(x+y)g(x-y)=f(x)^2-f(y)^2 \\ g(x+y)g(x-y)=f(x)^2-f(y)^2$$, which does not use his iteration method.