• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.925-932
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• 1996

On certain groupoids called LIR-groupoids, one can define abstract definitions of continuity and differentiation of functions. Many properties of this abstract continuity and differentiation have analogy to the ordinary continuity and differentiation of real-valued functions.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.137-143
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• 1995

First we recall some properties of the spaces $D_p$ and study the continuity of the operators on $D_p$. We also consider the continuity of the operations on the dual spaces $D'_p$ with the weak topology.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1261-1270
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• 2011

In this note we give conditions for continuity of spectrum, approximative point spectrum and defect spectrum on the set $\{T\}+\mathcal{K}(X)$, where $T{\in}\mathcal{B}(X)$ and $\mathcal{K}(X)$ is the set of compact operators.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.615-622
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• 2009

We solve the automatic continuity problem of an approximate higher derivation on a semisimple Banach algebra and investigate Hyers-Ulam stability for higher derivations.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.273-278
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• 1997

Let A be a Banach algebra and B a semisimple annifilator Banach algebra. Then every homomorphism from A into B with range is continuous. Also we obtain condition s for the automatic continuity of homomorphism with dense range.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.99-101
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• 1992

In this paper, we study some properties of sets of complete continuity. Moreover, we prove that if the subsets $C_1$ and $C_2$ of a Banach space X are sets of complete continuity, then so is the set $C_1{\times}C_2$ in the product space $X{\times}X$.

• East Asian mathematical journal
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• v.27 no.5
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• pp.565-572
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• 2011

In this paper we prove common fixed point of weakly compatible maps without continuity in Menger spaces. We show that continuity of any mapping is not required for the existence of fixed point. We improve some earlier results.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.207-216
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• 2024

This note is devoted to establishing the variation continuity of the one-dimensional discrete uncentered multilinear maximal operator. The above result is based on some refine variation estimates of the above maximal functions on monotone intervals. The main result essentially improves some known ones.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.591-603
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• 2006

For a set $X{\subset}{\mathbb{Z}}^n$ let $(X,\;T^n_X)$ be the subspace of the Khalimsky n-dimensional space $({\mathbb{Z}}^n,\;T^n)$, $n{\in}N$. Considering a k-adjacency of $(X,\;T^n_X)$, we use the notation $(X,\;k,\;T^n_X)$. In this paper for a map $$f:(X,\;k,\;T^n_X){\rightarrow}(Y,\;2\;T_Y)$$, we find the condition that weak (k, 2)-continuity of the map f implies strong (k, 2)-continuity of f.

• Journal of Korea Society of Digital Industry and Information Management
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• v.6 no.3
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• pp.203-209
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• 2010

Since information systems are pervasive in the business and non-business areas, the issue of extending researches on information systems to knowledge systems and e-business systems is one of the most profitable topics of researches. We propose a historical, discontinuous changes introducing ambiguity in explaining and interpreting innovative nature of three paradigms of systems: information systems, knowledge systems, and e-business systems. Resorting to the historical perspective in developing ideas into meaningful themes, we proposed a discrete continuity in interpreting changes of paradigms of systems. Discrete continuity may be explained by ambiguously-shared meaningful perspectives applied to different paradigms of systems and interpretive elements of each system. The discrete continuity has been adopted to make ambiguity utilized have instrumental contribution in researches. The engrafted ambiguity in systems design, development, and use could have enduring instrumental value in interpreting the types or variants of systems in each paradigm of systems.