• 대한수학회보
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• 제42권1호
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• pp.133-148
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• 2005

In this paper, we obtain the general solution of a gen-eralized quadratic and additive type functional equation f(x + ay) + af(x - y) = f(x - ay) + af(x + y) for any integer a with a $\neq$ -1. 0, 1 in the class of functions between real vector spaces and investigate the generalized Hyers- Ulam stability problem for the equation.

• Korean Journal of Mathematics
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• 제22권2호
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• pp.339-348
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• 2014

In this paper, we investigate the solution of the following functional inequality $${\parallel}f(x)+f(y)+f(az),\;w{\parallel}{\leq}{\parallel}f(x+y)-f(-az),\;w{\parallel}$$ for some xed non-zero integer a, and prove the generalized Hyers-Ulam stability of it in non-Archimedean 2-normed spaces.

• 대한수학회논문집
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• 제28권2호
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• pp.269-283
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• 2013

In this paper, we investigate a stability of the functional equation $$\sum^3_{i=0}_3C_i(-1)^{3-i}f(ix+y)=0$$ by using the fixed point theory in the sense of L. C$\breve{a}$dariu and V. Radu.

• Korean Journal of Mathematics
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• 제17권3호
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• pp.315-330
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• 2009

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quadratic functional equation $$(0.1)\;\frac{1}{2}(f(2x+y)+f(2x-y)-f(-2x-y)-f(y- 2x))\\{\hspace{35}}=2f(x+y)+2f(x-y)+4f(x)-8f(-x)-2f(y)-2f(-y)$$ in fuzzy Banach spaces.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.556-559
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• 1996

In this paper, we suggest a H center .inf. generalized predictive control(H center GPC) which guarantees $H_{\infty}$-norm bounds. THe suggested control is obtained by solving the min-max problem in nonrecursive forms. The stability conditions of the suggested control are derived in a somewhat simple form and it is not required for the derived solution to be a saddle point solution. It is also shown that the suggested control guarantees the $H_{\infty}$-norm bounds under the same conditions of stability.

• 충청수학회지
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• 제18권1호
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• pp.41-49
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• 2005

In this paper, we prove the generalized Hyers-Ulam- Rassias stability of the functional equation $$af(\frac{x+y+z}{b})+af(\frac{x-y+z}{b})+af(\frac{x+y-z}{b})+af(\frac{-x+y+z}{b})=cf(x)+cf(y)+cf(z)$$.

• 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.

• 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.

• 충청수학회지
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• 제21권1호
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• pp.129-138
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• 2008

In this paper we introduce a Jensen type cubic functional equation $$f\(\frac{3x+y}{2}\)+f\(\frac{x+3y}{2}\)\\=12f\(\frac{x+y}{2}\)+2f(x)+2f(y),$$ and then investigate the generalized Hyers-Ulam stability problem for the equation.

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