A Continuation Method for Weakly Kannan Maps. (26th January 2010)

• Record Type: Journal Article
• Authors: Ariza-Ruiz, David; Jiménez-Melado, Antonio
• Other Names: Khamsi Mohamed A. Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2010(2010)
• Publication Date: 2010-01-26
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2010/321594
• Languages: English
• ISSNs: 1687-1812

Abstract

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.