Abstract
The notions of strong continuity of Levine (Amer. Math. Monthly 67(1960), 269) and perfect continuity due to Noiri (Indian J. Pure Appl. Math. 15(3) (1984), 241-250) are extended to the framework of multifunctions. Basic properties of strongly continuous and upper (lower) perfectly continuous multifunctions are studied and their place in the hierarchy of variants of continuity of multifunctions is discussed. The class of upper (lower) perfectly continuous multifunctions properly contains the class of strongly continuous multifunctions and is strictly contained in the class of upper (lower) cl-supercontinuous multifunctions (Applied Gen. Topol.)[5]. Examples are included to reflect upon the distinctiveness of the notions so introduced from the ones that already exist in the mathematical literature. In the process we extend several known results in the literature including those of Ekici, Singh and others to the realm of multifunctions.