This paper is devoted to introduce and study new kinds of FP-multifunctions, namely FP-lower (upper) α-continuous, FP-lower (upper) almost α-continuous, and FP-lower (upper) weakly α-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.
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