# Common Fixed Point Theorem for Expansive Mappings in G-metric Spaces

Volume 6, Issue 1, pp 60--71
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### Authors

R. K. Vats - National Institute of Technology, Hamirpur (H.P.)-177005. S. Kumar - DCR University of Science and Techonology Murthal, Sonepat (Haryana). V. Sihag - National Institute of Technology, Hamirpur (H.P.)-177005.

### Abstract

In this paper, we introduce the concept of compatible and compatible mapping of type (A) in G-metric space akin to compatible and its type (A) in metric space introduced by Jungck [7] and Jungck et.al [8] and then establishes an example to show their independency. Further, we prove a common fixed point theorem for two pair of expansive mappings which generalize and unify the results of Wang et.al. [19] and Daffer et.al. [17]. Examples are given to support the generality of our result. Finally, we elaborate our theorem as an application in product space.

### Share and Cite

##### ISRP Style

R. K. Vats, S. Kumar, V. Sihag, Common Fixed Point Theorem for Expansive Mappings in G-metric Spaces, Journal of Mathematics and Computer Science, 6 (2013), no. 1, 60--71

##### AMA Style

Vats R. K., Kumar S., Sihag V., Common Fixed Point Theorem for Expansive Mappings in G-metric Spaces. J Math Comput SCI-JM. (2013); 6(1):60--71

##### Chicago/Turabian Style

Vats, R. K., Kumar, S., Sihag, V.. "Common Fixed Point Theorem for Expansive Mappings in G-metric Spaces." Journal of Mathematics and Computer Science, 6, no. 1 (2013): 60--71

### Keywords

• G-metric space
• fixed point
• compatible mapping of type (A)
• $\phi$ function of contractive modulus.

•  54H25
•  54E35

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