Menger probabilistic G-metric-like space and fixed point theorems

Volume 9, Issue 6, pp 4263--4276 http://dx.doi.org/10.22436/jnsa.009.06.68

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Authors

Yanxia Lu - Department of Mathematics and physics, North China Electric Power University, Baoding 071003, China. Xiaoying Gong - Department of Mathematics and Sciences, Shijiazhuang University of Economics, Shijiazhuang 050031, China. Xiaomin Xu - School of Economics and Management, North China Electric Power University, Beijing 102206, China.

Abstract

In this paper, we first introduce a concept called Menger probabilistic G-metric-like space which is a generalization of Menger probabilistic metric-like space of Hierro and Sen. Some fixed point theorems for various kinds of contractions in framework of this space are given. Our results extend some recent ones of Zhou et al., Hua et al. and Alsulami et al.. Finally, an example is given to illustrate the main result of this paper.

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Keywords

• Menger space
• fixed point
• \(\varphi\)-contraction
• metric-like space.

MSC

•  47H05
•  47H09

References

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