Abstract:In this paper, we give necessary and sufficient conditions for a point in a Musielak-Orlicz sequence space equipped with the Orlicz norm to be an {H}-point. We give necessary and sufficient conditions for a Musielak-Orlicz sequence space equipped with the Orlicz norm to have the {Kadec-Klee} property, the uniform {Kadec-Klee} property and to be nearly uniformly convex. We show that a Musielak-Orlicz sequence space equipped with the Orlicz norm has the fixed point property if and only if it is reflexive.
Keywords: nearly uniformly convex, uniform Kadec-Klee property, Kadec-Klee property, Musielak-Orlicz sequence space, fixed point property
AMS Subject Classification: 46E30, 46B20, 47H10