• Bulletin of the Korean Mathematical Society
• /
• v.61 no.4
• /
• pp.1137-1159
• /
• 2024

In the paper, we prove that if a continuous map of a compact uniform space is equicontinuous and pointwise topologically stable, then it is persistent. We also show that if a sequence of uniformly expansive continuous maps of a compact uniform space has a uniform limit and the uniform shadowing property, then the limit is topologically stable. In addition, we introduce the concepts of shadowable points and topologically stable points for a continuous map of a compact topological space and obtain that every shadowable point of an expansive continuous map of a compact topological space is topologically stable.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.343-351
• /
• 2013

In this paper, the dynamics on a transcendental entire semigroup G is investigated. We show the possible values of any limit function of G in strictly wandering domains and Fatou components, respectively. Moreover, if G is of class $\mathfrak{B}$, for any $z$ in a Fatou domain, there does not exist a sequence $\{g_k\}$ of G such that $g_k(z){\rightarrow}{\infty}$ as $k{\rightarrow}{\infty}$.

• Kyungpook Mathematical Journal
• /
• v.53 no.3
• /
• pp.479-495
• /
• 2013

Taking the weighted geometric mean [11] on the cone of positive definite matrix, we propose an iterative mean algorithm involving weighted arithmetic and geometric means of $n$-positive definite matrices which is a weighted version of Carlson mean presented by Lee and Lim [13]. We show that each sequence of the weigthed Carlson iterative mean algorithm has a common limit and the common limit of satisfies weighted multidimensional versions of all properties like permutation symmetry, concavity, monotonicity, homogeneity, congruence invariancy, duality, mean inequalities.

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.983-992
• /
• 1996

Let p(x, dy) be a transition probability function on $(S, \rho)$, where S is a complete separable metric space. Then a Markov process $X_n$ which has p(x, dy) as its transition probability may be generated by random iterations of the form $X_{n+1} = f(X_n, \varepsilon_{n+1})$, where $\varepsilon_n$ is a sequence of independent and identically distributed random variables (See, e.g., Kifer(1986), Bhattacharya and Waymire(1990)).

• Journal of the Korean Mathematical Society
• /
• v.60 no.5
• /
• pp.1043-1055
• /
• 2023

In this paper we study a pointwise version of Walters topological stability in the class of homeomorphisms on a compact metric space. We also show that if a sequence of homeomorphisms on a compact metric space is uniformly expansive with the uniform shadowing property, then the limit is expansive with the shadowing property and so topologically stable. Furthermore, we give examples to illustrate our results.

• Journal of the Chungcheong Mathematical Society
• /
• v.37 no.2
• /
• pp.75-80
• /
• 2024

In this paper, we study some dynamics of the uniform limits of sequences in dynamical systems on a noncompact metric space. We show that if a sequence of homeomorphisms on a noncompact metric space has the uniform ergodic shadowing property, then the uniform limit also has the ergodic shadowing property. Then we apply this result to nonwandering maps.

• Communications of the Korean Mathematical Society
• /
• v.20 no.3
• /
• pp.579-588
• /
• 2005

In this paper we study the asymptotics for the energy density in the self-dual Chern-Simons CP(1) model. When the sequence of corresponding multivortex solutions converges to the topological limit, we show that the field configurations saturating the energy bound converges to the limit function. Also, we show that the energy density tends to be concentrated at the vortices and antivortices as the Chern-Simons coupling constant $\kappa$ goes to zero.

• Journal of the Korean Mathematical Society
• /
• v.43 no.3
• /
• pp.529-538
• /
• 2006

In this paper we derive the central limit theorem for ${\sum}^n_{i=l}\;a_{ni}{\xi}_{i},\;where\;\{a_{ni},\;1\;{\le}\;i\;{\le}n\}$ is a triangular array of non-negative numbers such that $sup_n{\sum}^n_{i=l}\;a^2_{ni}\;<\;{\infty},\;max_{1{\le}i{\le}n\;a_{ni}{\to}\;0\;as\;n{\to}{\infty}\;and\;{\xi}'_{i}s$ are a linearly positive quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process of the form $X_n\;=\;{\sum}^{\infty}_{j=-{\infty}}a_{k+j}{\xi}_{j}$.

• Communications of the Korean Mathematical Society
• /
• v.20 no.3
• /
• pp.531-538
• /
• 2005

In this paper we derive the central limit theorem for ${\sum}_{i=1}^n\;a_{ni}\xi_i$, where ${a_{ni},\;1\;{\leq}\;i\;{\leq}\;n}$ is a triangular array of nonnegative numbers such that $sup_n{\sum}_{i=1}^n\;a_{ni}^2\;<\;{\infty},\;max_{1{\leq}i{\leq}n}a_{ni}{\rightarrow}0\;as\;n\;{\rightarrow}\;{\infty}\;and\;\xi'_i\;s$ are a linearly negative quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process $X_n\;=\;\sum_{j=-\infty}^\infty\;a_k+_j{\xi}_j$.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.3
• /
• pp.615-623
• /
• 2013

In this paper we establish a central limit theorem for weighted sums of $Y_n={\sum_{i=1}^{n}}a_n,_iX_i$, where $\{a_{n,i},\;n{\in}N,\;1{\leq}i{\leq}n\}$ is an array of nonnegative numbers such that ${\sup}_{n{\geq}1}{\sum_{i=1}^{n}}a_{n,i}^2$ < ${\infty}$, ${\max}_{1{\leq}i{\leq}n}a_{n,i}{\rightarrow}0$ and $\{X_i,\;i{\in}N\}$ is a sequence of linear negatively quadrant dependent random variables with $EX_i=0$ and $EX_i^2$ < ${\infty}$. Using this result we will obtain a central limit theorem for partial sums of linear processes.