Fixed point results for probabilistic \(\varphi\)-contractions in generalized probabilistic metric spaces

Volume 8, Issue 6, pp 1150--1165 http://dx.doi.org/10.22436/jnsa.008.06.24

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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].

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Keywords

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

MSC

•  47H10
•  54E70

References

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