Banach Contraction Principle for Cyclical Mappings on Partial Metric Spaces
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Date
2012
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Springer international Publishing Ag
Open Access Color
GOLD
Green Open Access
Yes
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No
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Top 10%
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Abstract
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 (Ilic 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.
Description
Alzabut, Prof. Dr. Jehad/0000-0002-5262-1138; Mukheimer, Aiman/0000-0001-8798-3297; Abdeljawad, Thabet/0000-0002-8889-3768
Keywords
Partial Metric Space, Fixed Point, Cyclic Mapping, Banach Contraction Principle, 0-Compact Set, Banach space, Metric (unit), Economics, Applied Mathematics, General Topology (math.GN), Pure mathematics, Cone Metric Spaces, Contraction principle, Discrete mathematics, Contraction mapping, Fixed Point Theorems in Metric Spaces, Operations management, Physical Sciences, FOS: Mathematics, Contraction (grammar), Medicine, Differential geometry, Geometry and Topology, Metric space, Fixed-point theorem, Internal medicine, Mathematics, Mathematics - General Topology, 0-compact set, Special maps on metric spaces, Fixed-point and coincidence theorems (topological aspects), partial metric space, cyclic mapping, fixed point, Banach contraction principle
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Citation
Abdeljawad, T...et al. (2012). Banach contraction principle for cyclical mappings on partial metric spaces. Fixed Point Theory And Applications, 154, 1-7. http://dx.doi.org/10.1186/1687-1812-2012-154
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Scopus Q
Q2
OpenCitations Citation Count
9
Source
Fixed Point Theory and Applications
Volume
2012
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