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

Volume 10, Issue 7, pp 3939--3962 http://dx.doi.org/10.22436/jnsa.010.07.46

Publication Date: July 27, 2017 Submission Date: October 28, 2016

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Authors

Jingfeng Tian - College of Science and Technology, North China Electric Power University, Baoding, Hebei Province, 071051, P. R. China. Ximei Hu - China Mobile Group Hebei Co., Ltd., Baoding, Hebei Province, 071000, P. R. China.

Abstract

In this paper, we present some new fixed point and common fixed point (common coupled fixed point, common tripled fixed point, and common quadruple fixed point) theorems of probabilistic contractions with a gauge function \(\varphi\) in generalized probabilistic metric spaces proposed by Zhou et al. [C.-L. Zhou, S.-H. Wang, L. Ćirić, S. M. Alsulami, Fixed Point Theory Appl., 2014 (2014), 15 pages]. Our results extend some existing results. Moreover, an example is given to illustrate our main results.

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Keywords

• Coupled fixed point
• fixed point
• metric space
• probabilistic \(\varphi\)-contractions
• gauge function.

MSC

•  47H10
•  54E70

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