• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.347-359
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• 2016

In this paper, we show that the solutions to perturbed functional differential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$, have a bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of $t_{\infty}$-similarity.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.447-454
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• 2014

Two necessary and sufficient conditions for the oscillation of the bounded solutions of the second-order nonlinear delay differential equation $$(a(t)x^{\prime}(t))^{\prime}+q(t)f(x[{\tau}(t)])=0$$ are obtained by constructing the sequence of functions and using inequality technique.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.747-761
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• 2017

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determining estimates on the operator norm, and showing there are no isometries.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.209-215
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• 2000

Let X be a locally convex space. A series of clearcut characterizations for the boundedness of vector measure $\mu{\;}:{\;}\sum\rightarrow{\;}X$ is obtained, e.g., ${\mu}$ is bounded if and only if ${\mu}(A_j){\;}\rightarrow{\;}0$ weakly for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$ and if and only if $\{\frac{1}{j^j}{\mu}(A_j)\}^{\infty}_{j=1}$ is bounded for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1577-1586
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• 2018

In this paper, we prove that if every bounded ${\mathcal{A}}$-harmonic function on a complete Riemannian manifold M is asymptotically constant at infinity of p-nonparabolic ends of M, then each bounded ${\mathcal{A}}$-harmonic function is uniquely determined by the values at infinity of p-nonparabolic ends of M, where ${\mathcal{A}}$ is a nonlinear elliptic operator of type p on M. Furthermore, in this case, every bounded ${\mathcal{A}}$-harmonic function on M has finite energy.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.79-90
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• 2004

In this paper the authors present sufficient conditions for all bounded solutions of the second order neutral difference equation ${\Delta}^2(y_n\;-\;py_{n-{\kappa}})\;-\;q_nf(y_{n-e})\;=\;0,\;n\;{\in}\;N$ to be oscillatory. Examples are provided to illustrate the results.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.1-8
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• 1995

Since the concept of Pettis integral was introduced in 1938 [10], the Pettis integrability of weakly measurable functions has been studied by many authors [5, 6, 7, 8, 9, 11]. It is known that there is a bounded function that is not Pettis integrable [10, Example 10. 8]. So it is natural to raise the question: when is a bounded function Pettis integrable\ulcorner(omitted)

• Honam Mathematical Journal
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• v.35 no.2
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• pp.129-136
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• 2013

Let G be a commutative group which is 2-divisible, $\mathbb{R}$ the set of real numbers and $f,g:G{\rightarrow}\mathbb{R}$. In this article, we investigate bounded solutions of the Pexider-exponential functional inequality ${\mid}f(x+y)-f(x)g(y){\mid}{\leq}{\epsilon}$ for all $x,y{\in}G$.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.773-786
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• 2023

In this paper, we introduce the pseudospectra of bounded linear operators on quasi normed space and study its proprieties. Beside that, we establish the relationship between the pseudospectra of a sequence of bounded linear operators and its limit.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.19-27
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• 1995

In 1974 H.Herrlich invented nearness spaces, a very fruitful concept which enables one to unify topological aspects. In this paper, we introduce the Lindel$\ddot{o}$f nearness structure, countably bounded nearness structure and countably totally bounded nearness structure. And we show that (X, ${\xi}_L$) is concrete and complete if and only if ${\xi}_L={\xi}_t$ in a symmetric topological space (X, t). Also we show that the following are equivalent in a symmetric topological space (X, t): (1) (X, ${\xi}_L$) is countably totally bounded. (2) (X, ${\xi}_t$) is countably totally bounded. (3) (X, t) is countably compact.