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

  • A. K. Mirmostafaee

Abstract

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.
Published
25.09.2017
How to Cite
Mirmostafaee, A. 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.
Section
Research articles