Abstract
In this paper, we introduce the concept of the Z-M-PN space, and obtain some new fixed point theorems in probabilistic metric spaces. Meanwhile, some famous fixed point theorems are generalized in probabilistic metric spaces, such as fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Zhang Shi-sheng,Fixed Point Theory and Application, Chongqing Press, Chongqing (1984), (in Chinese).
Zhang Shi-sheng and Chen Yu-qing, Topological degree theory and fixed point theorems in probabilistic metric spaces,Applied Mathematics and Mechanics (English Ed.),10, 6 (1989), 495–505.
Cao Jue-sheng and Lin Yi-qi, The extension theorem and topological degree of compact continuous operators on a probabilistic normed linear space,Journal of Nanjing Normal University 14, 1 (1991), 1–8. (in Chinese)
Gong Huai-yun, The achievement and prospect in the research of probabilistic metric spaces in China.The Literature Contributed by Experts at the Academic Symposium of the China's Fifth Session of Fixed Point, Probabilistic Metric Space and Variational in Equalities (5, 1991). (in Chinese)
Xia Dao-xing et al.,Real Variable Function Theory and Functional Analysis (Vol. II), The Publishing House of People's Education, Beijing (1979), (in Chinese)
Li Guo-zhen, On generalization of Guo's theorem,Journal of Jiangxi Normal University,2 (1984), 10–12. (in Chinese)
Ding Guang-gui,An Introduction to Banach Space Theory, Science Press (1984). (in Chinese)
Guo Da-jun, Some fixed point theorems and applications,Nonlinear Anal.,10 (1986), 1293–1302.
Sun Jing-xian, A generalization of Guo's theorem and applications,J. Math. Anal. Appl.,126 (1987).
Zhu Chuan-xi, Several new mappings of expansion and fixed point theorems,Journal of Jiangxi Normal University, 3 (1991), 244–248. (in Chinese)
Li Guo-zhen, Zhu Chuan-xi, Iterative technique for quasiweakly continuous nonlinear operator equations,The Literature Contributed by Experts at the Academic Symposium of the China's Fifth Session of Fixed Point, Probabilistic Metric Space and Variational Inequalities (5, 1991), 8–14. (in Chinese)
Author information
Authors and Affiliations
Additional information
Communicated by Zhang Shi-sheng
Projects supported by Provincial Natural Science Foundation of Jiangxi, China First Received May 31, 1993.
Rights and permissions
About this article
Cite this article
Chuan-xi, Z. Some new fixed point theorems in probabilistic metric spaces. Appl Math Mech 16, 179–185 (1995). https://doi.org/10.1007/BF02451457
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02451457