半序概率度量空间中压缩条件下的三元重合点定理

刘建辉, 朱传喜, 吴照奇

数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 517-526.

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数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 517-526. DOI: 10.12386/A2014sxxb0049
论文

半序概率度量空间中压缩条件下的三元重合点定理

    刘建辉, 朱传喜, 吴照奇
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Tripled Coincidence Point Theorems under Contractive Conditions in Partially Ordered Probabilistic Metric Spaces

    Jian Hui LIU, Chuan Xi ZHU, Zhao Qi WU
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摘要

在完备的半序概率度量空间中建立了自映射对G:X×X×X→X与 g:X→X,满足一定非线性压缩条件下的三元重合点与三元不动点定理,所得结果推广了已有文献中的若干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应用.

Abstract

We establish tripled coincidence point and tripled fixed point theorems for a pair of self-mappings G:X×X×X→X与 g:X→X, satisfying a nonlinear contractive condition in partially ordered complete probabilistic metric spaces. The obtained results generalize some coupled coincidence and coupled common fixed point theorems in the corresponding literatures. Finally, an example is given to illustrate our main results.

关键词

三元重合点 / 三元不动点 / 半序集 / 混合G-单调映射

Key words

tripled coincidence point / tripled fixed point / partially ordered set

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刘建辉, 朱传喜, 吴照奇. 半序概率度量空间中压缩条件下的三元重合点定理. 数学学报, 2014, 57(3): 517-526 https://doi.org/10.12386/A2014sxxb0049
Jian Hui LIU, Chuan Xi ZHU, Zhao Qi WU. Tripled Coincidence Point Theorems under Contractive Conditions in Partially Ordered Probabilistic Metric Spaces. Acta Mathematica Sinica, Chinese Series, 2014, 57(3): 517-526 https://doi.org/10.12386/A2014sxxb0049

参考文献

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基金

国家自然科学基金资助项目（11071108，11361042，1132609）；江西省自然科学基金项目（2010GZS0147）及江西省教育厅青年基金项目（GJJ13012）

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