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

Dinesh Panthi¹, Kanhaiya Jha², Pavan Kumar Jha³, P. Sumati Kumari⁴

¹Department of Mathematics, Valmeeki Campus, Nepal Sanskrit University, Kathmandu, Nepal.
²Department of Natural Sciences (Mathematics), Kathmandu University, Dhulikhel, Nepal.
³Department of Mathematics, Amrit Science Campus, Tribhuvan University, Kathmandu, Nepal.
⁴Department of Mathematics, K L University, Vaddeswaram, India.

DOI: 10.4236/ajcm.2015.52009                

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.

Keywords

d-Metric Space, Common Fixed Point, Weakly Compatible, Contractive Modulus, Cauchy Sequence

Conflicts of Interest

The authors declare no conflicts of interest.

References

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