Copyright © 2010 David Ariza-Ruiz and Antonio Jiménez-Melado. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The first continuation method for contractive maps in the setting of a metric space was given by Granas. Later, Frigon extended Granas theorem to the class of weakly contractive maps, and recently Agarwal and O'Regan have given the corresponding result for a certain type of quasicontractions which includes maps of Kannan type. In this note we introduce the concept of weakly Kannan maps and give a fixed point theorem, and then a continuation method, for this class of maps.