International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 1-16

Some fixed point iteration procedures

B. E. Rhoades

Department of Mathematics, Indiana University, Bloomington 47405, IN, USA

Received 15 August 1989

Copyright © 1991 B. E. Rhoades. 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.


This paper provides a survey of iteration procedures that have been used to obtain fixed points for maps satisfying a variety of contractive conditions. The author does not claim to provide complete coverage of the literature, and admits to certain biases in the theorems that are cited herein. In spite of these shortcomings, however, this paper should be a useful reference for those persons wishing to become better acquainted with the area.