• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• 호남수학학술지
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• 제29권4호
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• pp.543-554
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• 2007

In this paper, we prove the stability of a mixed type functional equation f( -x + y + z) + f(x - y + z) + f(x + y - z) = f(x - y) + f(y - z) + f(z - x) + f.(x) + f(y) + f(z).

• Korean Journal of Mathematics
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• 제16권3호
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• pp.369-378
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• 2008

The aim of this paper is to study the stability problem for the pexider type trigonometric functional equation f(x + y) − f(x−y) = 2g(x)h(y), which is related to the d'Alembert, the Wilson, the sine, and the mixed trigonometric functional equations.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권1호
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• pp.23-35
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• 2007

We investigate the modified Hyers-Ulam-Rassias stability for the following mixed type functional equation, i.e, cubic or quadratic type functional equation : 9f(x+y)-9f(x-y)+f(6y)=3f(x+3y)-3f(x-3y)+9f(2y).

• 호남수학학술지
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• 제34권1호
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• pp.19-34
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• 2012

In this paper, we investigate the stability of a functional equation f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z) = 0 by using the fixed point theory in the sense of L. Cadariu and V. Radu.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권1호
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• pp.59-71
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z)=0$$. by using a fixed point theorem in the sense of L. C$\breve{a}$dariu and V. Radu.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.91-101
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• 2015

In this paper, we investigate the stability of the functional equation f(-x + y + z + w) + f(x - y + z + w) + f(x + y - z + w) + f(x + y + z - w) = 3f(x) + f(-x) + 3f(y) + f(-y) + 3f(z) + f(-z) + 3f(w) + f(-w) by using the direct method in the sense of Hyers.

• 호남수학학술지
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• 제32권1호
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• pp.29-43
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• 2010

In this note, by using the fixed point method, we prove the generalized stability for a mixed type functional equation in random normed spaces of which the general solution is either cubic or quadratic.

• 충청수학회지
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• 제22권4호
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• pp.815-830
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• 2009

In this paper we establish the general solution of the following functional equation with mixed type of quadratic and additive mappings f(mx+y)+f(mx-y)+2f(x)=f(x+y)+f(x-y)+2f(mx), where $m{\geq}2$ is a positive integer, and then investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.

• Korean Journal of Mathematics
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• 제17권4호
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• pp.419-428
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• 2009

We show the existence of at least one nontrivial solution of the homogeneous mixed type nonlinear elliptic problem. Here mixed type nonlinearity means that the nonlinear part contain the jumping nonlinearity and the critical growth nonlinearity. We first investigate the sub-level sets of the corresponding functional in the Soboles space and the linking inequalities of the functional on the sub-level sets. We next investigate that the functional I satisfies the mountain pass geometry in the critical point theory. We obtain the result by the mountain pass method, the critical point theory and variational method.