Journal of the
Korean Mathematical Society JKMS

We give a generalization of the selection theorem of Ben-El-Mechaiekh and Oudadess to complete $LD$-metric spaces with the aid of the notion of $n$-connectedness. Our new selection theorem is used to obtain new results on fixed points and coincidence points for compact lower semicontinuous set-valued maps with closed values consisting of $\Cal D$-sets in a complete $LD$-metric space.

Keywords: Selection theorem, $n$-connected, paracompact, $LD$-metric space, lower semicontinuous set-valued map, coincidence point, fixed point

MSC numbers: 54C65, 54C60, 55M20