• 충청수학회지
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• 제29권4호
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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.

• 대한수학회지
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• 제43권5호
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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.

• 대한수학회보
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• 제58권3호
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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.

• 충청수학회지
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• 제32권4호
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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.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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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.

• Korean Journal of Mathematics
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• 제27권4호
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• pp.1119-1131
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• 2019

In this paper, we introduce the notion of generalized f-derivation of lattice implication algebra and investigate some related properties. Also, we prove that if D is a generalized f-derivation associated with an f-derivation d of L, then D(x → y) = f(x) → D(y) for all x, y ∈ L.

• East Asian mathematical journal
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• 제36권1호
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• pp.1-11
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• 2020

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

• 충청수학회지
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• 제32권2호
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• pp.179-189
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• 2019

In this paper, we introduce the notion of symmetric bi-generalized derivation of lattice implication algebra L and investigated some related properties. Also, we prove that a map $F:L{\times}L{\rightarrow}L$ is a symmetric bi-generalized derivation associated with symmetric bi-derivation D on L if and only if F is a symmetric map and it satisfies $F(x{\rightarrow}y,z)=x{\rightarrow}F(y,z)$ for all $x,y,z{\in}L$.

• 충청수학회지
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• 제26권2호
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• pp.357-365
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• 2013

Fix $n-2$ elements $h_1,{\cdots},h_{n-2}$ of the quotient field B of the polynomial algebra $\mathbb{C}[x_1,x_2,{\cdots},x_n]$. It is proved that B is a Poisson algebra with Poisson bracket defined by $\{f,g\}=det(Jac(f,g,h_1,{\cdots},h_{n-2})$ for any $f,g{\in}B$, where det(Jac) is the determinant of a Jacobian matrix.

• 대한수학회보
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• 제33권3호
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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 $C^t to C$.