• 충청수학회지
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• 제22권2호
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• pp.251-259
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• 2009

We investigate the multiple solutions for the nonlinear parabolic boundary value problem with jumping nonlinearity crossing two eigenvalues. We show the existence of at least four nontrivial periodic solutions for the parabolic boundary value problem. We restrict ourselves to the real Hilbert space and obtain this result by the geometry of the mapping.

• 충청수학회지
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• 제28권4호
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• pp.635-645
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• 2015

We will show the general solution of the functional equation $$\begin{eqnarray}f(x+ay)+f(x-ay)+2(a^2-1)f(x)\\=a^2f(x+y)+a^2f(x-y)+2a^2(a^2-1)f(y)\end{eqnarray}$$ and investigate the Hyers-Ulam stability of the quartic set-valued functional equation.

• 대한수학회보
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• 제44권4호
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• pp.825-840
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• 2007

In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• 대한수학회논문집
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• 제24권1호
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• pp.67-83
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• 2009

Several common fixed point theorems for a few contractive type mappings in complete metric spaces are established. As applications, the existence and uniqueness of common solutions for certain systems of functional equations arising in dynamic programming are discussed.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권3호
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• pp.109-124
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• 2020

We establish coincidence point theorem for S-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. With the help of obtain result, we derive two dimensional results for generalized compatible pair of mappings F, G : X² → X. As an application, we obtain the solution of integral equation and also give an example to show the usefulness of our results. Our results improve, sharpen, enrich and generalize various known results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권4호
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• pp.389-401
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• 2015

We will show the general solution of the functional equation f(x + ay) + f(x − ay) + 2(a² − 1)f(x) = a²f(x + y) + a²f(x − y) + 2a²(a² − 1)f(y) and investigate the stability of quartic Lie *-derivations associated with the given functional equation.

• 호남수학학술지
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• 제20권1호
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• pp.135-145
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• 1998

In this paper, we focus on the convex-valued selection theorem out of four main selection theorems; zero-dimensional, convex-valued, compact-valued, finite-dimensional theorems based on Michael's papers. We prove some theorems about lower semi-continuous set-valued mappings, and derive some applications to closed continuous set-valued mappings and to functional analysis. We also give a partial solution to the open problem posed by Engelking, Heath, and Michael.

• 충청수학회지
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• 제21권2호
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• pp.165-174
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• 2008

In this paper, we obtain the general solution, the generalized Hyers-Ulam-Rassias stability, and the stability by using the alternative fixed point for a cubic functional equation $4f(x+my)+4f(x-my)+m^2f(2x)=8f(x)+4m^2f(x+y)+4m^2f(x-y)$ for a positive integer $m{\geq}2$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권3호
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• pp.297-306
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• 2009

In this paper, we obtain the general solution and the generalized HyersUlam stability theorem for an additive functional equation $af(x+y)+2f({\frac{x}{2}}+y)+2f(x+{\frac{y}{2})=(a+3)[f(x)+f(y)]$for any fixed integer a.

• 대한수학회논문집
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• 제13권4호
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• pp.765-773
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• 1998

Let E be a smooth Banach space. Suppose T : E longrightarrow E is a strongly accretive map. It is proved that each of the two well known fixed point iteration methods (the Mann and Ishikawa iteration methods), under suitable conditions, converges strongly to a solution of the equation Tx = f.