• 대한수학회지
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• 제32권1호
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• pp.141-149
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• 1995

Let N denote the set of positive integers. Fix $d_1, d_2 \in N with d = d_1 + d_2$. Let X and Y be real random variables and let ${X_i : i \in N^d_1} and {Y_j : j \in N^d_2}$ be independent families of independent identically distributed random variables with $L(X) = L(X_i) and L(Y) = L(Y_j)$, where $L(\cdot)$ denote the law of $\cdot$.

• 대한수학회지
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• 제52권2호
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• pp.373-388
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• 2015

In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a finite family of nonexpansive mappings in Hilbert space. Strong convergence theorem is proved for the sequence generated by the scheme. Finally, a parallel iterative algorithm for two finite families of variational inequalities and nonexpansive mappings is established.

• 대한수학회지
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• 제42권2호
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• pp.269-289
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• 2005

An infinite system of stochastic differential equations (SDE)driven by Brownian motions and compensated Poisson random measures for the locations and weights of a collection of particles is considered. This is an analogue of the work by Kurtz and Xiong where compensated Poisson random measures are replaced by white noise. The particles interact through their weighted measure V, which is shown to be a solution of a stochastic differential equation. Also a limit theorem for system of SDE is proved when the corresponding Poisson random measures in SDE converge to white noise.

• Journal of the Korean Statistical Society
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• 제30권1호
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• pp.21-30
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• 2001

Suppose we observe a set of data (X$_1$,Y$_1$(, …, (X$_{n}$,Y$_{n}$) and use the Nadaraya-Watson regression estimator to estimate m(x)=E(Y│X=x). in this article bandwidth selection problem for the Nadaraya-Watson regression estimator is investigated. In particular cross validation method based on average square error(ASE) is considered. Theoretical results here include a central limit theorem that quantifies convergence rates of the bandwidth selector.tor.

• 대한수학회보
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• 제38권3호
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• pp.587-603
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• 2001

The purpose of this paper is to study the nonlinear ergodic theorems and asymptotic behavior for an almost-orbit of asymptotically nonexpansive type mappings in a uniformly convex Banach space with Opial’s condition.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.301-307
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• 2008

Let $R_n$ be the the first return time to its initial n-word. Then the Ornstein-Weiss first return time theorem implies that log$R_n$ divided by n converges to entropy. We consider the convergence of log$R_n$ for Sturmian sequences which has the lowest complexity. In this case, we normalize the logarithm of the first return time by log n. We show that for any numbers $1{\leq}{\alpha},\;{\beta}{\leq}{\infty}$, there is a Sturmian sequence of which limsup is ${\alpha}$ and liminf is $1/{\beta}$.

• 충청수학회지
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• 제21권1호
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• pp.21-28
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• 2008

In this paper, we give the Riemann-type extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We prove that a function f is C-Dunford integrable if and only if $x^*f$ is C-integrable for each $x^*{\in}X^*$ and prove the controlled convergence theorem for the C-Pettis integral.

• East Asian mathematical journal
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• 제34권3호
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• pp.265-285
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• 2018

The main purpose of this paper, by using the resolvent operator technique associated with randomly (A, ${\eta}$, m)-accretive operator is to establish an existence and convergence theorem for a class of system of random nonlinear equations with fuzzy mappings in Banach spaces. Our works are improvements and generalizations of the corresponding well-known results.

• East Asian mathematical journal
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• 제26권3호
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• pp.337-350
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• 2010

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

• 대한수학회지
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• 제36권3호
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• pp.581-592
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• 1999

Let M be a properly immersed timelike hypersurface of $\overline{M}$. If M is a diagonal type, M satisfies the generic condition under the certain conditions of the eigenvalues of the shape operator. Moreover, applying them to Raychaudhuri equation, we can show that M satisfies the generic condition. Thus, by these results, we establish the singularity theorem for M in $\overline{M}$.