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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Generalization of Banach Contraction Principle in Two Directions

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

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.

Journal of Mathematics and Statistics
Volume 3 No. 3, 2007, 112-115

DOI: https://doi.org/10.3844/jmssp.2007.112.115

Published On: 30 September 2007

How to Cite: El-Shobaky, E., Ali, S. M. & Ali, M. S. (2007). Generalization of Banach Contraction Principle in Two Directions. Journal of Mathematics and Statistics, 3(3), 112-115. https://doi.org/10.3844/jmssp.2007.112.115

Open AccessCopyright: © 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.

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Keywords

  • {a,b,c}-contraction mapping
  • Banach contraction principle
  • weakly Cauchy normed spaces