• 대한수학회논문집
• /
• 제19권2호
• /
• pp.321-328
• /
• 2004

In this paper, we will prove the following: Let D be a nonempty of a normed linear space X and T : D -> X be a nonexpansive mapping. Let ${x_n}$ be a sequence in D and ${t_n}$, ${s_n}$ be real sequences such that (i) $0\;{\leq}\;t_n\;{\leq}\;t\;<\;1\;and\;{\sum_{n=1}}^{\infty}\;t_n\;=\;{\infty},\;(ii)\;(a)\;0\;{\leq}\;s_n\;{\leq}\;1,\;s_n\;->\;0\;as\;n\;->\;{\infty}\;and\;{\sum_{n=1}}^{\infty}\;t_ns_n\;<\;{\infty}\;or\;(b)\;s_n\;=\;s\;for\;all\;n\;{\geq}\;1\;and\;s\;{\in}\;[0,1),\;(iii)\;x_{n+1}\;=\;(1-t_n)x_n+t_nT(s_nTx_n+(1-s_n)x_n)\;for\;all\;n\;{\geq}\;1.$ Then, if the sequence {x_n} is bounded, then $lim_{n->\infty}\;$\mid$$\mid$x_n-Tx_n$\mid$$\mid$\;=\;0$. This result improves and complements a result of Deng [2]. Furthermore, we will show that certain conditions on D, X and T guarantee the weak and strong convergence of the Ishikawa iterative sequence to a fixed point of T.

• Kyungpook Mathematical Journal
• /
• 제62권1호
• /
• pp.1-28
• /
• 2022

In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ_r.

• 대한수학회보
• /
• 제23권2호
• /
• pp.103-111
• /
• 1986

In [2] and [3], the Shinwon polynomial S$_{n}$(x) of order n is defined and studied in some details. In this paper we will define the general Shinwon polynomial S$_{n}$(a,x) and the Dickson polynomial D$_{n}$(a,x) of the second kind of order n which is a slightly changed form of the Dickson polynomial g$_{n}$(a,x), and show that D$_{n}$(a,x) is closely related to S$_{n}$(a,x).EX> n/(a,x).

• 대한수학회지
• /
• 제33권4호
• /
• pp.891-908
• /
• 1996

Let (X,d) be a metric space and let T be a mapping from X into itself. We say that a metric space (X,d) is T-orbitally complete if every Cauchy sequence of the form ${T^{n_i}x}_{i \in N}$ for $x \in X$ converges to a point in X.

• Korean Journal of Mathematics
• /
• 제22권1호
• /
• pp.91-121
• /
• 2014

Let X and Y be vector spaces. It is shown that a mapping $f:X{\rightarrow}Y$ satisfies the functional equation ${\ddag}$ $$2df(\frac{x_1+{\sum}_{j=2}^{2d}(-1)^jx_j}{2d})-2df(\frac{x_1+{\sum}_{j=2}^{2d}(-1)^{j+1}x_j}{2d})=2\sum_{j=2}^{2d}(-1)^jf(x_j)$$ if and only if the mapping $f:X{\rightarrow}Y$ is additive, and prove the Cauchy-Rassias stability of the functional equation (${\ddag}$) in Banach modules over a unital $C^*$-algebra, and in Poisson Banach modules over a unital Poisson $C^*$-algebra. Let $\mathcal{A}$ and $\mathcal{B}$ be unital $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras. As an application, we show that every almost homomorphism $h:\mathcal{A}{\rightarrow}\mathcal{B}$ of $\mathcal{A}$ into $\mathcal{B}$ is a homomorphism when $h(d^nuy)=h(d^nu)h(y)$ or $h(d^nu{\circ}y)=h(d^nu){\circ}h(y)$ for all unitaries $u{\in}\mathcal{A}$, all $y{\in}\mathcal{A}$, and n = 0, 1, 2, ${\cdots}$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras, and of Lie $JC^*$-algebra derivations in Lie $JC^*$-algebras.

• 한국의학물리학회지:의학물리
• /
• 제13권1호
• /
• pp.27-31
• /
• 2002

6MeV 전자선의 output 인자를 결정하기 위해 간편하게 output 인자를 예측하는 수단인 1D(Dimension) 방법을 이용하였으며 그리고 1D 방법으로 결정된 output 인자를 개별적 beam cutout 하에서 직접 측정한 output 인자와 비교하여 1D 방법의 정확성을 분석하였다. 1D 방법은 정방형 field의 한 변과 항상 동일한 한 변을 갖는 사각형 field의 output 인자로서 규정되며, 임의의 사각형 field (X,Y)의 output은 1D output 인자의 곱으로 주어진다. 6MeV 전자선의 대단히 큰 정방형 field의 output은 1D 방법을 사용하면 실제보다 높은 값을 나타내지만 교정인자 CF=C.[(X-10)(Y-10)/$\mid$(X-10)(Y-10)$\mid^{1/2}]$를 적용하면 개별적 cutout하에 직접 측정된 output 인자와 잘 일치하였으며 그 오차 범위는 1% 이내였다.

• Korean Journal of Mathematics
• /
• 제23권4호
• /
• pp.631-636
• /
• 2015

Let D be an integral domain and w be the so-called w-operation on D. In this note, we introduce the notion of *(w)-domains: D is a *(w)-domain if $(({\cap}(x_i))({\cap}(y_j)))_w={\cap}(x_iy_j)$ for all nonzero elements $x_1,{\ldots},x_m$; $y_1,{\ldots},y_n$ of D. We then show that D is a $Pr{\ddot{u}}fer$ v-multiplication domain if and only if D is a *(w)-domain and $A^{-1}$ is of finite type for all nonzero finitely generated fractional ideals A of D.

• 대한수학회논문집
• /
• 제9권2호
• /
• pp.423-438
• /
• 1994

We employ the Galerkin method to solve the nonlinear Urysohn integral equation (1.1) x(t) = f(t) ＋ $∫_{D}$ k(t, s, x(s))ds (t $\in$ D), where D is a bounded domain in $R^{d}$ , the function f and k are known and x is the solution to be determined. We assume that D has a locally Lipschitz boundary ([1, p. 67]). We can rewrite (1.1) in operator notation as x = f ＋ Kx. We consider (1.1) as an operator equation on $L_{\infty$}$(D) and assume that K is defined on the closure $\Omega$ of a bounded open set $\Omega$ ⊂ $L_{\infty}$(D). Throughout our analysis we put the following assumptions on (1.1).(omitted)(1.1).(omitted)

• 대한수학회지
• /
• 제35권4호
• /
• pp.981-997
• /
• 1998

We shall show first general Metivier operators ${D_y}^2+(x^{2l}+y^{2k}){D_x}^2,l,k=1,2,....,have {G_{x,y}}^{{\theta,d}}$-hypoellipticity in the vicinity of the origin (0,0), where $\theta=\frac{l(1+k)}{l(1+k)-k},\;d=\frac{\theta+k}{1+k}$ (＞1), and finally the optimality of these exponents {$\theta$, d} will be shown.

• 한국세라믹학회지
• /
• 제40권7호
• /
• pp.644-651
• /
• 2003

첨가물의 형태가 X7R용 MLCC 유전 원료의 전기적 특성 및 미세구조에 미치는 영향을 평가하였다. Glass frit 및 산화물 형태로 제조된 첨가물을 분말 공정 조건을 달리하여 동일한 주조성에 첨가하였다. 미세구조 및 유전특성을 측정한 결과, glass 층에 dopant의 농도 구배가 존재하는 조성이 유전 특성이 가장 우수하였다. 최적 조성을 MLCC로 제작하여 유전 특성을 측정하였으며, X7R 제반 조건을 만족하였다.