Abstract. On the unit ball of an Orlicz function space the (weak star) denting points and (weak star) quasi-denting points coincide. But in Orlicz sequence space the (weak star) quasi-denting points are different from (weak star) denting points. We also show that in Orlitz space the weak star drop property and the Kadec-Klee property are equivalent. Hence the weak drop property and the weak star drop property are independent in Banach spaces.

AMS Subject Classification (1991): 46B20, 46E30

Received August 6, 1996 and in revised form March 7, 1997. (Registered under 5781/2009.)