# Caristis fixed point theorem on $C^*$-algebra valued metric spaces

Volume 9, Issue 2, pp 584--588 Publication Date: February 23, 2016
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### Authors

Dur-e Shehwar - Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan. Samina Batul - Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan. Tayyab Kamran - Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan. Adrian Ghiura - Department of Mathematics and Informatics, University Politehnica of Bucharest, Bucharest, 060042, Romania.

### Abstract

We present the extension of Caristi's fixed point theorem for mappings defined on $C^*$-algebra valued metric spaces. We prove the existence of fixed point using the concept of minimal element in $C^*$-algebra valued metric space by introducing the notion of partial order on X.

### Keywords

• Caristi's theorem
• $C^*$-algebra
• metric space.

•  47H10
•  54H25

### References

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