Points of upper and lower semicontinuity of multivalued functions ..................
We investigate joint upper and lower semicontinuity of two-variable set-valued functions. More precisely. among other results, we show that, under certain conditions, a two-variable lower horizontally quasicontinuous mapping $F : X \times Y \rightarrow \scr K (Z)$ is jointly upper semicontinuous o...
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| Date: | 2017 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2017
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1772 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We investigate joint upper and lower semicontinuity of two-variable set-valued functions. More precisely. among other results, we show that, under certain conditions, a two-variable lower horizontally quasicontinuous mapping $F : X \times Y \rightarrow \scr K (Z)$ is jointly upper semicontinuous on sets of the from $D \times \{ y_0\}$, where $D$ is a dense G\delta subset of $X$ and $y_0 \in Y$.
A similar result is obtained for the joint lower semicontinuity of upper horizontally quasicontinuous mappings. These
results improve some known results on the joint continuity of single-valued functions. |
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