Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 321594, 12 pages
doi:10.1155/2010/321594

A continuation method for weakly Kannan maps

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.