A Common Fixed Point Theorem for Two Pairs of Mappings in Dislocated Metric Space

Abstract

Dislocated metric space differs from metric space for a property that self distance of a point needs not to be equal to zero. This property plays an important role to deal with the problems of various disciplines to obtain fixed point results. In this article, we establish a common fixed point theorem for two pairs of weakly compatible mappings which generalize and extend the result of Brain Fisher [1] in the setting of dislocated metric space with replacement of contractive constant by contractive modulus for which continuity of mappings is not necessary and compatible mappings by weakly compatible mappings.

Share and Cite:

Panthi, D. , Jha, K. , Jha, P. and Kumari, P. (2015) A Common Fixed Point Theorem for Two Pairs of Mappings in Dislocated Metric Space. American Journal of Computational Mathematics, 5, 106-112. doi: 10.4236/ajcm.2015.52009.

Conflicts of Interest

The authors declare no conflicts of interest.

 [1] Fisher, B. (1983) Common Fixed Point of Four Mappings. Bulletin of the Institute of Mathematics Academia Sinica, 11, 103-113. [2] Banach, S. (1922) Sur les operations dans les ensembles abstraits et leur applications aux equations integrals. Fundamenta Mathematicae, 3, 133-181. [3] Sessa, S. (1982) On a Weak Commutativity Condition of Mappings in a Fixed Point Considerations. Publications de l’Institut Mathematique (Beograd), 32, 149-153. [4] Jungck, G. (1986) Compatible Mappings and Common Fixed Points. International Journal of Mathematics and Mathematical Sciences, 9, 771-779. http://dx.doi.org/10.1155/S0161171286000935 [5] Jungck, G. and Rhoades, B.E. (1998) Fixed Points for Set Valued Functions without Continuity. The Indian Journal of Pure and Applied Mathematics, 29, 227-238. [6] Matthews, S.G. (1986) Metric Domains for Completeness. Technical Report 76, Ph.D. Thesis, Department of Computer Science, University of Warwick, Coventry. [7] Hitzler, P. and Seda, A.K. (2000) Dislocated Topologies. Journal of Electrical Engineering, 51, 3-7.