Meir-Keeler Α-Contractive Fixed and Common Fixed Point Theorems
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Abstract
Generalized Meir-Keeler alpha-contractive functions and pairs are introduced and their fixed and common fixed point theorems are obtained. Also, the so-called generalized Meir-Keeler alpha-f-contractive maps commuting with f are introduced and their coincidence and common fixed point theorems are investigated. New sufficient conditions different from those in (Samet et al. in Nonlinear Anal. 75:2154-2165, 2012) are used. An application to the coupled fixed point is established as well. An example is given to show that the alpha-Meir-Keeler generalization is real. AMS Subject Classification: 47H10, 54H25.
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Abdeljawad, Thabet/0000-0002-8889-3768
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Keywords
Orbitally Complete Metric Space, Common Fixed Point, Meir-Keeler Alpha-Contractive, Alpha-Admissible Mapping, Coupled Fixed Point, α-Admissible Mapping, Meir-Keeler α-Contractive, Alternative medicine, Fixed Point Theorems, Applied Mathematics, Generalization, Pure mathematics, Fixed point, Discrete mathematics, Generalized Contractions, Coincidence, Mathematical analysis, Coincidence point, Fixed Point Theorems in Metric Spaces, Contractive Mappings, Physical Sciences, FOS: Mathematics, Pathology, Medicine, Differential geometry, Geometry and Topology, Fixed-point theorem, Mathematics, coupled fixed point, \(\alpha\)-admissible mapping, Meir-Keller \(\alpha\)-contractive condition, Complete metric spaces, Special maps on metric spaces, orbitally complete metric space, Fixed-point and coincidence theorems (topological aspects), common fixed point
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02 engineering and technology, 01 natural sciences, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics
Citation
Abdeljawad, T. (2013). Meir-Keeler alpha-contractive fixed and common fixed point theorems. Fixed Point Theory And Applications, 1-3. http://dx.doi.org/10.1186/1687-1812-2013-19
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31
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2013
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