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

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Keywords

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