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

Reduced Assumption in the Banach Contraction Principle

Sahar M. Ali

Abstract

In this study we introduce a novel class of normed spaces called weakly Cauchy normed spaces not necessarily complete in general and proved the existence of a fixed point of contraction mappings in these spaces, this is weaker assumption than the completeness assumption imposed on the given normed space on the other side the contraction condition valid only on a closed convex subset of the given space.

Journal of Mathematics and Statistics
Volume 2 No. 1, 2006, 343-345

DOI: https://doi.org/10.3844/jmssp.2006.343.345

Submitted On: 19 October 2005 Published On: 31 March 2006

How to Cite: Ali, S. M. (2006). Reduced Assumption in the Banach Contraction Principle. Journal of Mathematics and Statistics, 2(1), 343-345. https://doi.org/10.3844/jmssp.2006.343.345

Open AccessCopyright: © 2006 Sahar M. 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

  • Reduced assumption
  • contraction mapping
  • Banach contraction principle
  • normed spaces