Fixed Point Theory and Applications 
Volume 2008 (2008), Article ID 649749, 8 pages
doi:10.1155/2008/649749
Research Article

Some Similarity between Contractions and Kannan Mappings

Misako Kikkawa1 and Tomonari Suzuki2

 1Department of Mathematics, Faculty of Science, Saitama University, 255 Shimo-Okubo, Sakura, Saitama 338-8570, Japan
2Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Tobata, Kitakyushu 804-8550, Japan
Received 11 October 2007; Accepted 13 November 2007

Recommended by J. R. L. Webb

Abstract

Contractions are always continuous and Kannan mappings are not necessarily continuous. This is a very big difference between both mappings. However, we know that relaxed both mappings are quite similar. In this paper, we discuss both mappings from a new point of view.