Fixed point theorems for two new types of cyclic weakly contractive mappings in partially ordered Menger PM-spaces

Volume 8, Issue 4, pp 412--422 http://dx.doi.org/10.22436/jnsa.008.04.13

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Authors

Wenqing Xu - Department of Mathematics, Nanchang University, 330031, Nanchang, China. Chuanxi Zhu - Department of Mathematics, Nanchang University, 330031, Nanchang, China. Zhaoqi Wu - Department of Mathematics, Nanchang University, 330031, Nanchang, China. Li Zhu - Department of Mathematics, Nanchang University, 330031, Nanchang, China.

Abstract

In this paper, we introduce the concepts of cyclic weakly (\(\psi,\phi\))-contractive mappings and cyclic weakly (\(C,\psi,\varphi\))-contractive mappings, and prove some fixed point theorems for such two types of mappings in complete partially ordered Menger PM-spaces. Some new results are obtained, which extend and generalize some fixed point results in metric and probabilistic metric spaces. Some examples are given to support our results.

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Keywords

• Menger PM-space
• partially ordered
• cyclic weakly contractive
• fixed point.

MSC

•  47H10
•  54H25
•  46B20

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