• Korean Journal of Mathematics
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• v.20 no.1
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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 $$2f(x+y)+f(x-y)+f(y-x)-f(2x)-f(2y)=0$$.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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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.

• East Asian mathematical journal
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• v.31 no.5
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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.

• Korean Journal of Mathematics
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• v.19 no.4
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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 $$f(x+2y)-2f(x+y)+2f(x-y)-f(x-2y)=0$$.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.253-266
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• 2004

In this note, by using the fixed point alternative, we investigate the modified Hyers-Ulam-Rassias stability for the following mixed type functional inequality which is either cubic or quadratic: $\parallel$8ｆ(x-3y) + 24f(x+y) + f(8y) -8〔f(x+3y) + 3f(x-y) + 2f(2y)〕$\parallel$$\leq$$\varphi$(x,y).

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.287-307
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• 2016

Using the fixed point method, we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in matrix fuzzy normed spaces.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.201-215
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• 2012

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

• The Pure and Applied Mathematics
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• v.14 no.1 s.35
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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).

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.51-63
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• 2012

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

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.219-232
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• 2013

In this paper, we investigate the stability of the functional equation $$f(x+2y)-2f(x+y)+2f(x-y)-f(x-2y)=0$$ by using the fixed point theory in the sense of L. C$\breve{a}$dariu and V. Radu.