In 1961, Levine  introduced the notion of weakly continuous functions. Popa and Smithson independently introduced the concept of weakly continuous multifunctions. Noiri introduced the concept of minimal structure on a nonempty set. Also they introduced the notion of mX -open set and mX -closed set and characterize those sets using mX -cl and mX -int operators respectively. Further they introduced m-continuous functions and studied some of its basic properties. Noiri and Popa  introduced and studied other forms of continuous multifunctions namely, slightly m-continuous multifunctions.