MORE MAPS FOR WHICH F(T) = F(Tn)

We continue our investigation of situations in which the fixed point sets for maps and their iterates are the same. In a previous paper [21] we demonstrated a number of situations in which the fixed point set of a map is the same as the fixed point set of each iterate of the map. We also investigated the same phenomenon for pairs of maps, with respect to common fixed points. In this paper we continue that study. In Section 1 we examine some contractive conditions involving pairs of commuting maps. In section 2 we examine some contractive conditions involving multivalued maps for which the ¿-metric is used. In section 3 we examine some contractive conditions on 2-metric spaces. Let F(T) denote the fixed point set of a map T. As in [21] we shall say that a map T has property P if F(T) = F(Tn) for each n G N. We shall say that a pair of maps S and T have property Q if F(S)nF(T) = F(Sn)DF(Tn) for each n G N. If Ti is a collections of maps, then, if flF(Tj) = nF(Tf ) we shall say that this collection has property R. An important consequence of this study is that none of these maps has any nontrivial periodic points.