2 results for “Banach contraction principle”

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Research ArticleOpen accessPhrase in the titleGeneralization of Banach Contraction Principle in Two DirectionsE. El-Shobaky, Sahar Mohamed Ali, Montaser Saudi AliWe 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, Vol. 3, Issue 3 · 30 Sep 2007 · 6,761 accessesView PDF Cite

Research ArticleOpen accessPhrase in the titleReduced Assumption in the Banach Contraction PrincipleSahar M. AliIn 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 … …Journal of Mathematics and Statistics, Vol. 2, Issue 1 · 31 Mar 2006 · 6,825 accessesView PDF Cite