Journal of Mathematics and Statistics

Generalization of Banach Contraction Principle in Two Directions

E. El-Shobaky, Sahar Mohamed Ali and Montaser Saudi Ali

DOI : 10.3844/jmssp.2007.112.115

Journal of Mathematics and Statistics

Volume 3, Issue 3

Pages 112-115

Abstract

We showed that the generalized contraction mapping defined on a closed convex subset of a weakly Cauchy normed space has a unique fixed point. Moreover, the sequence of iterates of any element in the domain of the given mapping is converging strongly to the fixed point of such a mapping.

Copyright

© 2007 E. El-Shobaky, Sahar Mohamed Ali and Montaser Saudi Ali. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.