# Common Fixed Point Theorems for a Pair of Mappings in Complex-valued Metric Spaces

Volume 6, Issue 1, pp 18--26 Publication Date: January 15, 2013
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### Authors

R. K. Verma - Department of mathematics, Govt. C.L.C. College Patan Distt.-Durg (C.G.) 491111, INDIA. H. K. Pathak - School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010, INDIA.

### Abstract

The purpose of this paper is to prove common fixed point theorems for a pair of mappings satisfying a quasi-contraction condition in a complex-valued metric space $(X, d)$. For this, we have defined the ‘max’ function for the partial order $\leq$ in complex-valued metric $d$.

### Keywords

• Common fixed point
• contraction mapping
• contractive condition
• Banach contraction condition
• Complex-valued metric space.

•  47H10
•  54H25

### References

• [1] A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex-valued metric spaces, Numerical Functional Analysis and Optimization, 3(3) (2011), 243-253

• [2] S. Banach, Sür les operations dans les ensembles abstraits et. leur application aux equations integrales, Fund. Math, 3 (1922), 133-181