• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권2호
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• pp.175-183
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• 2010

Using Darbo's fixed point theorem, we establish the existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

• 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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• 제23권3호
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• pp.393-399
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• 2015

W. Park [J. Math. Anal. Appl. 376 (2011) 193-202] proved the Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. But there are serious problems in the control functions given in all theorems of the paper. In this paper, we correct the statements of these results and prove the corrected theorems. Moreover, we prove the superstability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces under the original given conditions.

• 대한수학회보
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• 제40권2호
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• pp.253-267
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• 2003

In this paper we deal With the quadratic functional equation (equation omitted) deriving from an inequality of T. Popoviciu for convex functions. We solve this functional equation by proving that its solutions we the polynomials of degree at most two. Likewise, we investigate its stability in the spirit of Hyers, Ulam, and Rassias.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2004년도 춘계학술대회 학술발표 논문집 제14권 제1호
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• pp.133-136
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• 2004

This paper proposes a stability condition in affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties and then, introduces the design method of a fuzzy-model-based controller which guarantees the stability. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of linear matrix inequalities (LMIs).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권4호
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• pp.323-335
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• 2004

In this paper, we solve the general solution of a modified additive and quadratic functional equation f(χ + 3y) + 3f(χ-y) = f(χ-3y) + 3f(χ+y) in the class of functions between real vector spaces and obtain the Hyers-Ulam-Rassias stability problem for the equation in the sense of Gavruta.

• Management Science and Financial Engineering
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• 제14권1호
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• pp.65-86
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• 2008

In this paper, we have considered the multicriteria quadratic plant location problem. In addition to the allocation costs, the maintenance costs of the plants are also considered. The objective functions considered in this paper are quadratic in nature. The given problem is reduced to the problem with linear objective function. The method of Fernandez and Puerto (2003) is applied to solve the reduced problem. It is illustrated with help of examples. The effect of the change in the allocation and maintenance costs on allocation of plants to the clients has also been discussed.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.351-358
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• 2003

We prove the generalized Hyers-Ulam stability of a quadratic functional equation f($\chi$+ y + z) + f($\chi$) + f(y) + f(z) = f($\chi$+ y) + f(y + z) + f(z + $\chi$) for the functions defined between Banach modules over a Banach algebra.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.471-478
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• 2007

In this article we shall introduce several operators on the reproducing kernel spaces and investigate quadratic forms on the $\mathcal{l}^2$ space. Using these operators we shall obtain a particular solution of a system of quadratic equations(1.5). Finally we can find an approximate solution of(1.5) by optimization of a nonnegative biquadratic polynomial.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.91-103
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• 2007

In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ${\varphi}$ is defined by $f(x{\ast}y)+f(x{\ast}y^{-1})-2g(x)-2g(y)={\varphi}(x,y)$, $f(x{\ast}y)+g(x{\ast}y^{-1})-2h(x)-2k(y)={\varphi}(x,y)$, where (G, *) is a group, X is a real or complex Hausdorff topological vector space and f, g, h, k are functions from G into X.