• 한국콘텐츠학회논문지
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• 제2권4호
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• pp.93-98
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• 2002

함수 방정식은 연구원들이 함수 자체의 정확한 형태를 가정하지 않고 단순히 기본적인 함수의 성질만을 언급하는 한정적이지 않은 방정식을 통하여 일반적인 관점의 수학적 형상화를 공식화하는데 매우 중요한 구실을 하기 때문에 실험적인 학문에서 유용하다. 그러한 많은 함수 방정식 가운데에서 이 논문은 다소 일반화된 2차 함수 방정식을 선택해 해를 구하며 이 방정식의 안정성을 증명한다. a$^2$f((x+y/a))+b$^2$f((x-y/b)) = 2f(x)+2f(y)

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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• pp.65-80
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• 2010

In [17, 18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces: (0.1) f(x + y) + f(x - y) = 2f(x) + 2f(y), (0.2) f(ax + by) + f(ax - by) = $2a^2 f(x)\;+\;2b^2f(y)$ for nonzero real numbers a, b with $a\;{\neq}\;{\pm}1$.

• 충청수학회지
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• 제26권2호
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• pp.367-375
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• 2013

In this paper, we investigate the stability for the functional equation $$f(x+y+z)+f(x-y)+f(x-z)-f(x-y-z)-f(x+y)-f(x+z)=0$$ in non-Archimedean normed spaces.

• 호남수학학술지
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• 제39권3호
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• pp.417-430
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• 2017

In this paper, we investigate the stability of a functional equation $$2f(ax+by)+abf(x-y)+abf(y-x)-{\frac{2af((a+b)x)}{a+b}}-{\frac{bf((a+b)y)}{a+b}}-{\frac{bf(-(a+b)y)}{a+b}}=o$$ by applying the direct method in the sense of Hyers and Ulam.

• 충청수학회지
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• 제27권2호
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• pp.261-269
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• 2014

In this paper, using fixed point method, we prove the Hyers-Ulam stability of the following functional equation $$(k+1)f(x+y)+f(x+{\sigma}(y))+kf({\sigma}(x)+y)-2(k+1)f(x)-2(k+1)f(y)=0$$ with an involution ${\sigma}$ for a fixed non-zero real number k with $k{\neq}-1$.

• Korean Journal of Mathematics
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• 제20권1호
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• pp.19-31
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$2f(x+y)+f(x-y)+f(y-x)-f(2x)-f(2y)=0$$.

• Korean Journal of Mathematics
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• 제24권1호
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• pp.41-49
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• 2016

In this paper, using xed point method, we prove the Hyers-Ulam stability of the following functional equation $$\hspace{15}f+(x+y+z)+f({\sigma}(x)+y+z)+f(x+{\sigma}(y)+z)+f(x+y+{\sigma}(z))\\=4f(x)+4f(y)+4f(z)$$ with involution in paranormed spaces.

• 충청수학회지
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• 제22권4호
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• pp.757-770
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• 2009

In this paper, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation (0.1) f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f(-2y) - 4f(y) - 4f(-y) in Banach spaces.

• 호남수학학술지
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• 제35권1호
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• pp.93-100
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• 2013

In this paper, we investigate the stability for the functional equation $$2f(x+y)+f(x-y)+f(y-x)-f(2x)-f(2y)=0$$ in non-Archimedean normed spaces.

• Korean Journal of Mathematics
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• 제19권4호
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• pp.437-451
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• 2011

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(x+2y)-2f(x+y)+2f(x-y)-f(x-2y)=0$$.