Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 649749, 8 pages
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

Academic Editor: J. R. L. Webb

Copyright © 2008 Misako Kikkawa and Tomonari Suzuki. 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.


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.