半序概率度量空间中压缩条件下相容映射的三元重合点与三元不动点定理

数学物理学报 ›› 2016, Vol. 36 ›› Issue (1): 157-167.

半序概率度量空间中压缩条件下相容映射的三元重合点与三元不动点定理

罗婷^1,2, 朱传喜¹

1 南昌大学数学系南昌 330031;
2 南昌工学院民族教育学院南昌 330108

收稿日期:2015-08-13 修回日期:2015-12-20 出版日期:2016-02-25 发布日期:2016-02-25
作者简介:罗婷,xiaoxiaoluo_66@163.com;朱传喜,chuanxizhu@126.com
基金资助:
国家自然科学基金(11361042,11071108)和江西省自然科学基金(20132BAB201001,2010GZS0147)资助

Tripled Coincidence and Tripled Fixed Point Theorems for Compatible Mappings Under Contractive Conditions in Partially Ordered Probabilistic Metric Spaces

Luo Ting^1,2, Zhu Chuanxi¹

1 Department of Mathematics, Nanchang University, Nanchang 330031;
2 College of Ethnic Education, Nanchang Institute of Science & Technology, Nanchang 330108

Received:2015-08-13 Revised:2015-12-20 Online:2016-02-25 Published:2016-02-25
Supported by:
Supported by the NSFC (11361042, 11071108) and the NSF of Jiangxi Province of China (20132BAB201001, 2010GZS0147)

摘要/Abstract

摘要：

在半序概率度量空间中建立了映射对G:X×X×X→X与g:X→X的相容性概念.在不需要可交换的条件下,研究了相容映射在满足更一般的非线性压缩条件下的三元重合点与三元不动点问题,所得结果推广了已有文献中的二元重合点与二元公共不动点定理.最后,给出主要结果的一个具体应用.

关键词: 概率度量空间, 三元重合点, 三元不动点, 半序集, 混合g-单调映射

Abstract:

In this paper, we establish the notion of compatibility for a pair of mappings G:X×X×X→X and g:X→X in partially ordered probabilistic metric spaces. Under not necessary commutative conditions, some tripled coincidence and tripled common fixed point problems of compatible mappings satisfying a more general nonlinear contractive condition are studied. The obtained results generalize some coupled common fixed point theorems in the corresponding literatures. Finally, an example is given to illustrate our main results.

Key words: Probabilistic metric space, Tripled coincidence point, Tripled fixed point, Partially ordered set, Mixed g-monotone mapping

中图分类号:

O177.91

罗婷, 朱传喜. 半序概率度量空间中压缩条件下相容映射的三元重合点与三元不动点定理[J]. 数学物理学报, 2016, 36(1): 157-167.

Luo Ting, Zhu Chuanxi. Tripled Coincidence and Tripled Fixed Point Theorems for Compatible Mappings Under Contractive Conditions in Partially Ordered Probabilistic Metric Spaces[J]. Acta mathematica scientia,Series A, 2016, 36(1): 157-167.

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