Banach contraction principle for cyclical mappings on partial metric spaces

We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilić et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can no...

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Published in:Fixed point theory and algorithms for sciences and engineering 2012-09, Vol.2012 (1), p.1-7, Article 154
Main Authors: Abdeljawad, T, Alzabut, JO, Mukheimer, A, Zaidan, Y
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Decomposition
Differential Geometry
Mapping
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Metric space
Professor Anthony To-Ming Lau's contributions to the development of Fixed Point Theory and Applications
Theorems
Topology
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Summary:We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilić et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact. MSC: 47H10, 54H25.
ISSN:1687-1812
1687-1820
1687-1812
2730-5422
DOI:10.1186/1687-1812-2012-154