Common fixed point theorems for six self-maps in \(b\)-metric spaces with nonlinear contractive conditions

Volume 9, Issue 12, pp 5909--5930 http://dx.doi.org/10.22436/jnsa.009.12.02

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Authors

Liya Liu - Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China. Feng Gu - Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China.

Abstract

In the framework of a b-metric space, by using the compatible and weak compatible conditions of self- mapping pair, we discussed the existence and uniqueness of the common fixed point for a class of \(\phi\)-type contraction mapping, some new common fixed point theorems are obtained. In the end of the paper, we give some illustrative examples in support of our new results. The results presented in this paper extend and improve some well-known comparable results in the existing literature.

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Keywords

• \(b\)-metric space
• common fixed point
• compatible maps
• weak compatible maps.

MSC

•  47H10
•  54H25

References

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