Common Fixed Points of Expansive Mappings in Generalized Metric Spaces

 

Priya Shahi*¹, Jatinderdeep Kaur¹ and S. S. Bhatia¹

 

¹ School of Mathematics and Computer Applications, Thapar University, Patiala-147004, India * priya.thaparian@gmail.com

 

ABSTRACT

In this paper, we establish a common fixed point theorem for expansive mappings by using the concept of weak compatibility in the setting of G -metric spaces. This result generalizes the result of Ahmed [2] from 2-metric spaces to G -metric spaces by removing the condition of sequential continuity of the mappings. Further, we generalize and extend the theorem of §ahin and Telci [20] to G -metric spaces and thereby extending the theorem of Wang et al. [23] for a pair of mappings to G -metric spaces. Some comparative examples are constructed which illustrate the obtained results.

Keywords: Common fixed point, G -metric spaces, Weakly compatible, Expansive mapping.

 

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Acknowledgment

The first author, Junior Research Fellow (No. F. 216/2011 (SA-I) gratefully acknowledges the University Grants Commission, Government of India for financial support.

 

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