• 충청수학회지
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• 제20권4호
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• pp.465-476
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• 2007

The aim of this paper is to investigate the stability problem bounded by function for the generalized sine functional equations as follow: $f(x)g(y)=f(\frac{x+y}{2})^2-f(\frac{x+{\sigma}y}{2})^2\\g(x)g(y)=f(\frac{x+y}{2})^2-f(\frac{x+{\sigma}y}{2})^2$. As a consequence, we have generalized the superstability of the sine type functional equations.

• East Asian mathematical journal
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• 제34권5호
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• pp.693-702
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• 2018

In this paper, we consider the generalized Hyers-Ulam stability for the following additive-quadratic functional equation with involution $f(x+2y)-f(2x+y)+f(x+y)+f({\sigma}(x)+y)+f(x)-4f(y)-f({\sigma}(y))=0$ in non-Archimedean spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권4호
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• pp.267-276
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• 2019

In this paper, we investigate the stability of an additive-cubic-quartic functional equation f(x + 2y) - 4f(x + y) + 6f(x) - 4f(x - y) + f(x - 2y) - 12f(y) - 12f(-y) = 0 by applying the fixed point theory in the sense of L. Cădariu and V. Radu.

• Korean Journal of Mathematics
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• 제24권1호
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• pp.1-13
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• 2016

This paper shows that the solutions to the perturbed functional dierential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic property. To sRhow these properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system $y^{\prime}=f(t,y)$.

• 한국지능시스템학회논문지
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• 제4권2호
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• pp.9-12
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• 1994

Let X, Y be normed linear spaces, and let p$_{1}$, p.sub 2/ be lower semi-continuous fuzzy norms on X, Y respectively, and have the bounded supports on X, Y respectively. In this paper, we prove that if Y is conplete, the set of all fuzzy continuous linear maps from X into Y is a fuzzy complete fuzzy normed linear space.

• East Asian mathematical journal
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• 제31권5호
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• pp.627-634
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• 2015

In this paper, we investigate the following orthogonally additive-quadratic functional equation f(2x + y) - f(x + 2y) - f(x + y) - f(y - x) - f(x) + f(y) + f(2y) = 0. and prove the generalized Hyers-Ulam stability for it in orthogonality spaces by using the fixed point method.

• 충청수학회지
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• 제29권2호
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• pp.347-359
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• 2016

In this paper, we show that the solutions to perturbed functional differential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$, have a bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of $t_{\infty}$-similarity.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.295-306
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• 2006

In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of 2m or 2m + 1 symmetric positive solutions of fourth-order two point boundary value problem y(4)(t) - f(t, y(t), y"(t))= 0, y(0) = y(1) = y'(0) = y"(1)=0.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.261-265
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• 2017

Let X and Y be independent identically distributed nondegenerate random variables with common absolutely continuous probability distribution function F(x) and the corresponding probability density function f(x) and $E(X^2)$<${\infty}$. Put Z = max(X, Y) and W = min(X, Y). In this paper, it is proved that Z - W and Z + W or$(X-Y)^2$ and X + Y are independent if and only if X and Y have normal distribution.

• 대한수학회보
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• 제34권4호
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• pp.561-571
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• 1997

The general (continuous) solution and the asymptotic behaviors of the unbounded solution of the functional equation $f(x + y)^2 = af(x)f(y) + bf(x)^2 + cf(y)^2$ and the Hyers-Ulam stability of that functional equation for the case when a = 2 and b = c = 1 shall be investigated.