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

• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.788-791
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• 1999

In recent years, many studies have been conducted on fuzzy control since it can surpass the conventional control in several respects. In this paper, numerical stability analysis methodology for the singleton-type linguistic fuzzy control systems is proposed. The Proposed stability analysis is not the analytical method but the numerical method using the convex optimization technique of Quadratic Programming (QP) and Linear Matrix Inequalities (LMI).

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.73-81
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• 2015

In this paper, we present the general solution of the functional equation $$rf(\frac{x+y+z+w}{s})+rf(\frac{x+y-z-w}{s})+rf(\frac{x-y+z-w}{s})+rf(\frac{x-y-z+w}{s})=tf(x)+tf(y)+tf(z)+tf(w)$$ and improve the Hyers-Ulam stability of the equation.

• 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.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.265-285
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• 2016

In this paper, we introduce functional equations in G-normed spaces and we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in complete G-normed spaces by using the fixed point method.

• 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.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.571-592
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• 2022

By established a Banach space with the Hausdorff distance, we introduce the alternative fixed-point theorem to explore the existence and uniqueness of a fixed subset of Y and investigate the stability of set-valued Euler-Lagrange functional equations in this space. Some properties of the Hausdorff distance are furthermore explored by a short and simple way.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.10
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• pp.1508-1512
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• 2012

This paper presents a relaxed stability condition for continuous-time affine fuzzy system using fuzzy Lyapunov function. In the previous studies, stability conditions for the affine fuzzy system based on quadratic Lyapunov function have a conservativeness. The stability condition is considered by using the fuzzy Lyapunov function, which has membership functions in the traditional Lyapunov function. Based on Lyapunov-stability theory, the stability condition for affine fuzzy system is derived and represented to linear matrix inequalities(LMIs). And slack matrix is added to stability condition for the relaxed stability condition. Finally, simulation example is given to illustrate the merits of the proposed method.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.377-391
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• 2013

The main goal of this paper is to present the additional stability results of the following orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ for all $x,y,z$ with $x{\bot}y$, which has been introduced in the paper [11], in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.1
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• pp.31-35
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• 1999

In this paper, we consider the robust pole assignment and the upper bound of quadratic cost function for the linear systems with time-varying uncertainy. The considered uncertainties are both the norm bounded unstructured case and the structured case that has the matrix polytope type uncertain structure. We derve conditions that guarantee the robust pole assignment inside a disk in the L.H.P. and the robust stability. Also, we derive the upper bound of quadratic cost for thil pole assigned systems. Finally, we show the usefulness of our results by an example.