On Some Well Known Fixed Point Theorems in b-Metric Spaces

@article{Kir2013OnSW,
  title={On Some Well Known Fixed Point Theorems in b-Metric Spaces},
  author={Mehmet Kir and Hukmi Kiziltunç},
  journal={Turkish Journal of Analysis and Number Theory},
  year={2013},
  volume={1},
  pages={13-16}
}
In this paper, our purpose is to show that Kannan Type and Chatterjea type contractive mappings have unique fixed point in b-metric spaces. Also, we see surprisingly a way that contrary to the known (usual) metric spaces, any contraction mapping is not need to be a weak conraction mapping in b-metric spaces. 
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References

SHOWING 1-10 OF 12 REFERENCES
UNIQUE FIXED POINT THEOREM FOR WEAKLY C-CONTRACTIVE MAPPINGS
In this work we introduce the class of weakly c-contractive mappings. We establish that these mappings necessarily have unique fixed points in complete metric spaces. We support our result by anExpand
FIXED POINT THEORY FOR MULTIVALUED GENERALIZED CONTRACTION ON A SET WITH TWO b-METRICS
The purpose of this paper is to present some fixed point results for multivalued generalized contraction on a set with two b-metrics. The data dependence and the well-posedness of the fixed pointExpand
Contraction mappings in $b$-metric spaces
Some generalizations of well known Banach's fixed point theorem in so-called b-metric spaces are presented. 1991 Mathematics Subject Classification: 47H10 1. Some problems, particurarly the problemExpand
Iterative Approximation of Fixed Points
Pre-Requisites of Fixed Points.- The Picard Iteration.- The Krasnoselskij Iteration.- The Mann Iteration.- The Ishikawa Iteration.- Other Fixed Point Iteration Procedures.- Stability of Fixed PointExpand
Fixed-point theorems
Fundamental Fixed-Point Principles.- 1 The Banach Fixed-Point Theorem and Iterative Methods.- 1.1. The Banach Fixed-Point Theorem.- 1.2. Continuous Dependence on a Parameter.- 1.3. The SignificanceExpand
Nonlinear set-valued contraction mappings in b-metric spaces
A fixed point theorem for set valued quasicontractions in b-metric spaces, Fixed Point Theory and Applications
  • 2012
Unique fixed point theorem for weakly ccontractive mappings, Kathmandu
  • Univ. J. Sci, Eng and Tech,
  • 2009
Some Results on Fixed Points
...
1
2
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