Common Fixed Point Theorem for Weakly Compatible Mappings in Dislocated Metric Space

# Pradeep Kumar Dwivedi^{1}

^{1}Department of Mathematics, Sagar Institute of Research and Technology, Bhopal, Madhya Pradesh, India.**Abstract:** In this paper we have to prove a common fixed point theorem for two pairs of compatible maps in dislocated metric space which generalizes and improves similar fixed point results.

**Keywords:** Dislocated metric space, weakly compatible maps, common fixed point.

**Cite this article as:** Pradeep Kumar Dwivedi, *Common Fixed Point Theorem for Weakly Compatible Mappings in Dislocated Metric Space*, Int. J. Math. And Appl., vol. 9, no. 2, 2021, pp. 91-95.

**References**

- A. Isufati, Fixed Point Theorem in Dislocated Quasi-Metric Space, Applied Math. Sci., 4(5)(2010), 217-223.
- C. T. Aage and J. N. Salunke, The Results on Fixed Points theorems in Dislocated and Quasi-Metric Space, Applied Math. Sci., 2(59)(2008), 2941-2948.
- C. T. Aage and J. N. Salunke, Some Results of Fixed Point Theorem in Dislocated Quasi-Metric Spaces, Bull. Marathwada Math. Soc., 9(2)(2008), 4-5.
- F. M. Zeyada, G. H. Hassan and M. A. Ahmed, A Generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces, The Arabian J. Sci. Engg., 31(1A)(2006), 111-114.
- G. Jungck and B. E. Rhoades, Fixed Points For Set Valued Functions without Continuity, Indian J. Pure Appl. Math., 29(3)(1998), 227-238.
- K. Jha, K. P. R. Rao and D. Panthi, A Common Fixed Point Theorem For Four Mappings in Dislocated Quasi-Metric Space, Int. J. Math. Sci. Engg. Appls., 6(1)(2012), 417-424.
- K. P. R. Rao and P. Rangaswamy, Common Fixed Point Theorem for Four Mappings in Dislocated Quasi-metric Space, The Nepali Math. Sci. Report, 30(1-2)(2010), 70-75.
- P. Hitzler and A. K. Seda, Dislocated Topologies, J. Electr. Engg., 51(12/s)(2000), 3-7.
- P. Hitzler, Generalized Metrics and Topology in Logic Programming Semantics, Ph.D.Thesis, National University of Ireland,(University College, Cork), (2001).
- R. Shrivastava, Z. K. Ansari and M. Sharma, Some Results on Fixed Points in Dislocated and Dislocated Quasi-Metric Spaces, J. Advance Studies in Topology, 3(1)(2012), 25-31.
- S. K. Vats, Weakly Compatible Maps in Metric Spaces, J. Indian Math. Soc., 69(1-4)(2002), 139-143.