Points of upper and lower semicontinuity of multivalued functions ..................

  • A. K. Mirmostafaee


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.
How to Cite
MirmostafaeeA. K. “Points of Upper and Lower Semicontinuity of Multivalued Functions ..................”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 9, Sept. 2017, pp. 1224-31, http://umj.imath.kiev.ua/index.php/umj/article/view/1772.
Research articles