Abstract
This paper is devoted to introduce and study new kinds of FP-multifunctions, namely FP-lower (upper) alpha-continuous, FP-lower (upper) almost alpha-continuous, and FP-lower (upper) weakly alpha-continuous multifunctions. Various properties of these multifunctions were investigated. We provided the relationships between these multifunctions and presented contrary examples. Finally, we gave the conditions which make these multifunctions equivalent.