Fixed Point Theorems for Ciric's and Generalized Contractions in b-Metric Spaces
Main Article Content
Abstract
In this article we obtained b-metric variant of common fixed point results for Ciric's and generalized contractions. We have also proved some fixed point results for rational contractive type conditions in the context of b-metric space. A particular example is also given in the support of our established result regarding Ciric's type contraction.
Article Details
References
- Mohammad Akkouchi, A Common Fixed Point Theorem For Expansive Mappings Under Strict Implicit Conditions on b-Metric Spaces, Acta Univ. Palacki. Olomuc, Fac. rer. nat. Mathematica , 50(2011), 5-15,.
- H. Ayadi et al., A Fixed Point Theorem For Set Valued Quasi Contraction in b-Metric Spaces, Fixed point Theorey and Applications ,2012(2012), Article ID 88,.
- V. Berinde, Iterative Approximation of Fixed poins of Weak Contraction Using Picard Iteration, Non Linear Analysis Forum, 9(2004), 43-53.
- Lj. B. Ciric, A Generalization of Banach's contraction Principle, Proc.Amer.Math. Soc., 45 (1974), 267-273.
- S. Czerwik, Contraction Mappings in b-Metric Space, Acta Math inf Univ Ostravinsis, 1(1993), 5-11.
- S. Czerwik, Non Linear Set Value Contraction Mappings in b-Metric Spaces, Atti Sem Math Fis Univ Modina, 46(2)(1998), 263-273.
- B. K. Dass and S. Gupta, An Extension of Banach's Contraction Principle Through Rational Expression, Indian Journal of pure and Applied Mathematics, 6 (1975), 1455-1458.
- P. Hitzler, Generalized Metrics and Topology in Logic Programming Semantics. Ph.D. thesis, National Univeristy of Ireland, University College Cork, (2001).
- M. S. Khan, A Fixed Point Theorem For Metric Spaces, Rendiconti Dell' istituto di Mathematica dell' Universtia di tresti, Vol. 8 (1976), 69-72,.
- Mehmet Kir, Hukmi Kizitune, on Some Well Known Fixed Point Theorems in b-Metric Space, Turkish Journal of Analysis and Number Theory, vol, 1(2013), 13-16.
- B. E. Rohades, A Comparison of various Definition of Contractive Mappings, Transfer, Amer. Soc., 226(1977), 257-290.
- Madhu Shrivastava , Q. k. Qureshi and A. D. singh, A Fixed Point Theorem for Continuous Mapping in Dislocated Quasi Metric Space. International journal of Theoretical and Applied Sciences, 4(1)(2012), 39 - 40.