| 赋值Banach代数的锥度量空间中c-距离下的不动点定理 |
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| 引用本文： | 黄华平,邓冠铁. 赋值Banach代数的锥度量空间中c-距离下的不动点定理[J]. 北京大学学报(自然科学版), 2018, 54(4): 693-698. DOI: 10.13209/j.0479-8023.2017.184 |
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| 作者姓名： | 黄华平 邓冠铁 |
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| 作者单位： | 北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,北京100875;北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,北京100875 |
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| 基金项目： | 国家自然科学基金(11271045)资助 |
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| 摘 要： | 在不考虑映射的连续性和锥的正规性条件下, 得到赋值Banach代数的锥度量空间中c-距离意义下压缩型映射不动点的存在性和唯一性定理, 在很大程度上改进和补充了前人的结果, 并举例验证了得到的结论。另外, 通过解决一个初等方程解的存在性和唯一性问题, 说明了所得结果的一个重要应用。
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| 关 键 词： | 赋值Banach代数的锥度量空间 c-距离 连续性 正规性 不动点 |
| 收稿时间： | 2017-04-05 |
Fixed Point Theorems under c-Distance in Cone Metric Spaces over Banach Algebras |
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| HUANG Huaping,DENG Guantie. Fixed Point Theorems under c-Distance in Cone Metric Spaces over Banach Algebras[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2018, 54(4): 693-698. DOI: 10.13209/j.0479-8023.2017.184 |
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| Authors: | HUANG Huaping DENG Guantie |
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| Affiliation: | Laboratory of Mathematics and Complex Systems (MOE), School of Mathematical Sciences, Beijing Normal University, Beijing 100875 |
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| Abstract: | The authors obtain several theorems of the existence and uniqueness of fixed point for contractive mappings under c-distance in cone metric spaces over Banach algebras without the assumptions of normality of cones and the continuity of mappings. The results greatly improve and complement some previous results. Moreover, a supportive example to illustrate the main assertions is also given. Otherwise, by solving the problem of existence and uniqueness for an elementary equation, a significant application for the obtained results is presented. |
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| Keywords: | cone metric space over Banach algebra c-distance continuity normality fixed point |
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