# Fixed point results for probabilistic $\varphi$-contractions in generalized probabilistic metric spaces

Volume 8, Issue 6, pp 1150--1165
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### Authors

Jing-Feng Tian - College of Science and Technology, North China Electric Power University, Baoding, Hebei Province, 071051, P. R. China. Xi-Mei Hu - China Mobile Group Hebei Co., Ltd., Baoding, Hebei Province, 071000, P. R. China. Guofang Zhang - College of Mathematics and Computer Science, Hebei University, Baoding, Hebei Province, 071000, P. R. China.

### Abstract

In this paper, we present some new fixed point theorems for probabilistic contractions with a gauge function $\varphi$ in generalized probabilistic metric spaces proposed by Zhou et al. Our theorems not only are generalizations of the corresponding results of Ćirić[L. Ćirić, Nonlinear Anal., 72 (2010), 2009-2018] and Jachymski [J. Jachymski, Nonlinear Anal., 73 (2010), 2199-2203], but also improve and extend the recent results given by Zhou et al. [C. Zhou, S. Wang, L. Ćirić, S. M. Alsulami, Fixed Point Theory Appl. 2014 (2014), 15 pages].

### Share and Cite

##### ISRP Style

Jing-Feng Tian, Xi-Mei Hu, Guofang Zhang, Fixed point results for probabilistic $\varphi$-contractions in generalized probabilistic metric spaces, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 6, 1150--1165

##### AMA Style

Tian Jing-Feng, Hu Xi-Mei, Zhang Guofang, Fixed point results for probabilistic $\varphi$-contractions in generalized probabilistic metric spaces. J. Nonlinear Sci. Appl. (2015); 8(6):1150--1165

##### Chicago/Turabian Style

Tian, Jing-Feng, Hu, Xi-Mei, Zhang, Guofang. "Fixed point results for probabilistic $\varphi$-contractions in generalized probabilistic metric spaces." Journal of Nonlinear Sciences and Applications, 8, no. 6 (2015): 1150--1165

### Keywords

• Fixed point
• metric space
• G-metric space
• nonlinear contractions
• gauge function.

•  47H10
•  54E70

### References

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