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MORE MAPS FOR WHICH F(T) = F(Tn) by G. S. Jeong; B. E. Rhoades is a Mathematics article available to read on EtoBox.

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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(T n ) for each n G N. We shall say that a pair of maps S and T have property 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. ## Commuting maps THEOREM 1.1. Let f and g be commuting selfmaps of a complete metric space (X,d), f continuous. Le

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Author

G. S. Jeong; B. E. Rhoades

Publisher

Walter de Gruyter GmbH; De Gruyter Open Ltd.; Warsaw: Faculty of Mathematics and Information Sciences of Warsaw University of Technology; Warsaw: De Gruyter (ISSN 0420-1213)

Published

2007

Language

EN

Field

Mathematics (Physical Sciences)