• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.1047-1063
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• 2006

Let $\varepsilon_#(X)$ be the subgroups of $\varepsilon(X)$ consisting of homotopy classes of self-homotopy equivalences that fix homotopy groups through the dimension of X and $\varepsilon_*(X) $ be the subgroup of $\varepsilon(X)$ that fix homology groups for all dimension. In this paper, we establish some connections between the homotopy group of X and the subgroup $\varepsilon_#(X)\cap\varepsilon_*(X)\;of\;\varepsilon(X)$. We also give some relations between $\pi_n(W)$, as well as a generalized Gottlieb group $G_n^f(W,X)$, and a subset $M_{#N}^f(X,W)$ of [X, W]. Finally we establish a connection between the coGottlieb group of X and the subgroup of $\varepsilon(X)$ consisting of homotopy classes of self-homotopy equivalences that fix cohomology groups.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.297-307
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• 2014

The present paper gives the notion of a derivation on a CI-algebra X and investigates related properties. We define a set $Fix_d(X)$ by $Fix_d(X)=\{x{\in}X{\mid}d(x)=x\}$, where d is a derivation on a CI-algebra X. We show that $Fix_d(X)$ is a subalgebra of X. Also, we prove some one-to-one and onto derivation theorems. Moreover, we study a regular derivation on a CI-algebra and an isotone derivation on a transitive CI-algebra.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.613-629
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• 2016

In this paper, we introduced the notion of multiplier of Boolean algebras and discuss related properties between multipliers and special mappings, like dual closures, homomorphisms on B. We introduce the notions of xed set $Fix_f(X)$ and normal ideal and obtain interconnection between multipliers and $Fix_f(B)$. Also, we introduce the special multiplier ${\alpha}_p$a nd study some properties. Finally, we show that if B is a Boolean algebra, then the set of all multipliers of B is also a Boolean algebra.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.753-762
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• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.

• The Journal of Korean Society for Radiation Therapy
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• v.22 no.1
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• pp.11-18
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• 2010

Purpose: In every time radiation therapy set up errors occur because internal anatomical organs move due to breathing and change of patient's position. These errors may affect the change of dose distribution between target area and normal structure. This study investigates the usefulness of body-fix in clinical treatment. Materials and Methods: Among 55~60 aged male patients who has hepatocellular carcinoma in area of liver's couinaud classification, we chose 10 patients and divided two groups by using body-fix or not. When applying body-fix, we maintained a vacuum of 80 mbar pressure by using vacuum pump (Medical intelligence, Germany). Patients had free breathing with supine position. After working to fuse and consist MV-CT (megavoltage computed tomography) with KV-CT (kilovoltage computed tomography) obtained by 5 times treatments, we compared and analyzed set up errors occurred to (Right to Left, RL) of X axis, (Anterioposterio, AP) of Z axis, (Cranicoudal, CC) of Y axis. Results: Average Set up errors through image fusion showed that group A moved $0.3{\pm}1.1\;mm$ (Cranicoudal, CC), $-1.1{\pm}0.7\;mm$ (Right to Left, RL), $-0.2{\pm}0.7\;mm$ (Anterioposterio, AP) and group B moved $0.62{\pm}1.94\;mm$ (Cranicoudal, CC), $-3.62{\pm}1.5\;mm$ (Right to Left, RL), $-0.22{\pm}1.2\;mm$ (Anterioposterio, AP). Deviations of X, Y and Z axis directions by applying body-fix indicated that maximum X axis was 5.5 mm, Y axis was 19.8 mm and Z axis was 3.2 mm. In relation to analysis of error directions, consistency doesn't exist for every patient but by using body-fix showed that the result of stable aspect in spite of changes of everyday's patient position and breathing. Conclusion: Using body-fix for liver cancer patient is considered effectively for tomotherapy. Because deviations between group A and B exist but they were stable and regular.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.93-102
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• 1997

Let C be a nonempty closed convex subset of a Banach space E and let $T_1, \cdots, T_N$ be nonexpansive mappings from C into itself (recall that a mapping $T : C \longrightarrow C$ is nonexpansive if $\left\$\mid$ Tx - Ty \right\$\mid$ \leq \left\$\mid$ x - y \right\$\mid$$ for all $x, y \in C$). We consider the fixed point problem for nonexpansive mappings : find a common fixed point, i.e., find a point in $\cap_{i=1}^N Fix(T_i)$, where $Fix(T_i) := {x \in C : x = T_i x}$ denotes the set of fixed points of $T_i$.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.247-254
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• 2018

In this paper, we introduce the notion of symmetric bi-multiplier of subtraction algebra and investigate some related properties. Also, we prove that if D is a symmetric bi-multiplier of X, then D is an isotone symmetric bi-multiplier of X.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.465-475
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• 1996

Fix t > 0. Denote by $C^t$ the space of $R$-valued continuous functions x on [0,t]. Let $C_0^t$ be the Wiener space - $C_0^t = {x \in C^t : x(0) = 0}$ - equipped with Wiener measure m. Let F be a function from $C^t to C$.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.441-451
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• 2019

In this paper, we introduce the notion of symmetric bi-f-derivation on subtraction algebra and investigated some related properties. Also, we prove that if D : X → X is a symmetric bi-f-derivation on X, then D satisfies D(x - y, z) = D(x, z) - f(y) for all x, y, z ∈ X.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.603-608
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• 2021

Fix k ≥ 3. If a multiplicative function f satisfies f(x₁ + x₂ + ⋯ + x_k) = f(x₁) + f(x₂) + ⋯ + f(x_k) for arbitrary positive triangular numbers x₁, x₂, …, x_k, then f is the identity function. This extends Chung and Phong's work for k = 2.