• Korean Journal of Mathematics
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• v.24 no.2
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• pp.297-305
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• 2016

In this paper, by using fixed point theorem, we obtain the stability of the following functional equations $$f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)f(p,q)h(r,s)\\f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)g(p,q)h(r,s)$$, where G is a commutative semigroup, ${\theta}:G^4{\rightarrow}{\mathbb{R}}_k$ a function and f, g, h are functionals on $G^2$.

• 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).

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.81-89
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• 2007

In this paper, we introduce the concept of a system of asymptotically quasinonexpansive type mappings. Furthermore, we define a $k$-step iterative sequence approximating common fixed point for a system of asymptotically quasi-nonexpansive type mappings and study its stability in real Banach spaces.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.313-326
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• 2015

In this paper, we present a fixed point method to prove generalized Hyers-Ulam stability of the systems of quadratic-cubic functional equations with constant coefficients in modular 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 $f(x+y+z+w)\;+\;2f(x)\;+\;2f(y)\;+\;2f(z)\;+\;2f(w)\;-\;f(x+y)\;-\;f(x+z)\;-\;f(x+w)\;-\;f(y+z)\;-\;f(y+w)\;-\;f(z+w)=0$.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.453-464
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• 2016

In this paper, we investigate the solution of the following functional inequality $$N(f(x)+f(y)+f(z),t){\geq}N(f(x+y+z),mt)$$ for some fixed real number m with $\frac{1}{3}$ < m ${\leq}$ 1 and using the fixed point method, we prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.

• 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 $$f(2x+y)+f(2x-y)+2f(x)-f(x+y)-f(x-y)-2f(2x)=0$$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.43-49
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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. $C\breve{a}dariu$ and V. Radu.

• 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.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.313-328
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• 2011

We investigate the stability of 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 by using a flxed point theorem in the sense of L. C$\breve{a}$adariu and V. Radu.