| 基于非线性压缩的Menger空间上不动点与不动度定理 |
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| 引用本文： | 靳鑫,肖建中.基于非线性压缩的Menger空间上不动点与不动度定理[J].南京气象学院学报,2013,5(5):472-477. |
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| 作者姓名： | 靳鑫 肖建中 |
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| 作者单位： | 南京信息工程大学 数学与统计学院, 南京, 210044;南京信息工程大学 数学与统计学院, 南京, 210044 |
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| 摘 要： | 首先,研究了Menger概率度量空间上的非线性算子,证明了非线性压缩与非线性扩张的不动点的存在唯一性;进一步将单个算子的不动点结果推广为一族可交换算子的公共不动点;最后,通过弱化条件,建立了模糊映射新的不动度定理.
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| 关 键 词： | Menger PM-空间 模糊映射 概率非线性压缩 不动点 不动度 |
| 收稿时间： | 2012/10/23 0:00:00 |
Fixed point and fixed degree theorems for nonlinear contraction in Menger spaces |
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| JIN Xin and XIAO Jianzhong.Fixed point and fixed degree theorems for nonlinear contraction in Menger spaces[J].Journal of Nanjing Institute of Meteorology,2013,5(5):472-477. |
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| Authors: | JIN Xin and XIAO Jianzhong |
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| Institution: | School of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing 210044;School of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing 210044 |
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| Abstract: | In this paper,we discuss the nonlinear operators in Menger probability metric spaces.We prove the existence and uniqueness of the fixed point for nonlinear contraction and expansion.Furthermore,we extend the result for single operator to common fixed point for a family of exchangeable operators.By weakening conditions,we establish a new fixed degree theorem for fuzzy mapping. |
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| Keywords: | Menger PM-space fuzzy mapping probabilistic nonlinear contraction fixed point fixed degree |
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