概率度量空间中若干新的不动点定理*
Some NeW Fixed point Theorems in Probabilistic Metric Spaces
-
摘要: 本文提出了Z-M-PN空间的概念,在概率度量空间中我们得到了若干新的不动点定理。同时,一些着名的不动点定理在概率度量空间中得到了推广,诸如:Schauder不动点定理、郭大钧不动点定理和Petryshyn不动点定理被推广到M-PN空间;Altman不动点定理被推广到Z-M-PN空间。Abstract: In this paper,we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Mean while,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.
-
Key words:
- topological degree /
- probabilistic metric spaces /
- operator /
- compact continuous operator /
- Z-M-PN space
-
[1] 张石生,《不动点理论及应用》,重庆出版社(1984), [2] 张石生、陈玉清,概率度量空间中的拓扑度理论与不动点定理.应用数学和力学,10(6)(1989),477-486, [3] 曹菊生、林颐铸,概率赋范线性空间中紧连续算子的延拓定理与拓扑度,南京师大学报,14(1)(1991),1-8, [4] 龚环云,我国在概率度量理论研究工作中均成果与履望,《全国第五届不动点、概率度最空间、变分不等式理论学术交流会文献》(1991,5), [5] 夏道行等四少、,《实变函数论与泛涵分析、(下册),人民教育出版社,北京(1979). [6] 李国祯,关于郭大钧定理时推广,江西师大学报,(2)(1984),10-12, [7] 定光桂,《巴拿赫空间引论》,科学出版社(1984), [8] Guo Da-jun,Some fixed point theorems and applications,Nonlinear Anal.,10(1986),1293-1302. [9] Sun Jing-xian,A generalization of Guo's theorem and application,J.Math.Anal.Appl.,126(1987) [10] 朱传喜,几类新的扩张映象及其不动点定理,江西师大学报,(3)(1991),244-248, [11] 李国祯、朱传喜,拟弱连续的算子方程迭代求解问题,《全国第五届不动点、概率度量空间与变分不等式理论学术交流会文献》(1991,5),8-14. -
计量
- 文章访问数: 2457
- HTML全文浏览量: 139
- PDF下载量: 711
- 被引次数: 0
下载:
渝公网安备50010802005915号