Inward contractions on metric spaces

We study the existence of constrained fixed points of contractions in arbitrary complete metric spaces from a global and local point of view. In particular, we provide generalizations of results due to Lim, Downing and Kirk and others. Some aspects of the topological transversality in the spirit of Frigon and Granas of contractions under constraints are also considered. © 2006 Elsevier Inc. All rights reserved.