• 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.

• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.461-494
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• 2024

We prove the Sobolev continuity of maximal commutator and its fractional variant with Lipschitz symbols, both in the global and local cases. The main result in global case answers a question originally posed by Liu and Wang in [29].

• 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.