2025年5月14日 19:16 星期三
首页 > 过刊浏览>2013年第5卷第5期 >472-477
PDF HTML阅读 XML下载 导出引用 引用提醒
基于非线性压缩的Menger空间上不动点与不动度定理
作者:

Fixed point and fixed degree theorems for nonlinear contraction in Menger spaces
Author:
  • 摘要
    • | |
  • 访问统计
    • |
  • 参考文献
    • |
  • 相似文献
    • |
  • 引证文献
    • | |
  • 文章评论
    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.

    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.

    参考文献
    [1] 张石生.概率度量空间的基本理论及应用(I)[J].应用数学和力学,1988,9 (2):117-126 ZHANG Shisheng.Basic theory and applications of probabilistic metric spaces (I)[J].Applied Mathematics and Mechanics,1988,9(2):117-126
    [2] Choudhury B S.A common unique fixed point result in metric spaces involving generalized altering distances[J].Mathematical Communications,2005,10(2):105-110
    [3] Ćiri ć L.Solving the Banach fixed point principle for nonlinear contractions in probabilistic metric spaces[J].Nonlinear Analysis:Theory,Methods & Applications,2010,72(3/4):2009-2018
    [4] Sehgal V M,Bharucha-Reid A T.Fixed points of contraction mappings on probabilistic metric space[J].Mathematical Systems Theory,1972,6(1/2):97-102
    [5] Fang J X.Common fixed point theorems of compatible and weakly compatible maps in Menger spaces[J].Nonlinear Analysis:Theory,Methods & Applications,2009,71(5/6):1833-1843
    [6] Choudhury B S,Das K,Dutta P N.A fixed point result in Menger spaces using a real function[J].Acta Mathematica Hungarica,2009,122(3):203-216
    [7] Jachymski J.On probabilistic -contractions on Menger spaces[J].Nonlinear Analysis:Theory,Methods & Applications,2010,73(7):2199-2203
    [8] Fang J X.Fixed degree for fuzzy mappings[J].Chinese Science Bulletin,1985,30(9):1267
    [9] Chang S-S.Fixed degree for fuzzy mappings and a generalization of Ky Fan theorem[J].Fuzzy Sets and Systems,1987,24(1):103-112
    [10] 张石生.关于Fuzzy映象的不动度[J].数学年刊A辑,1987,8(4):492-495 ZHANG Shisheng.On the fixed degree for fuzzy mappings[J].Chinese Annals of Mathematics (A),1987,8(4):492-495
    [11] Chang S-S,Cho Y J,Lee B S,et al.Fixed degree and fixed point theorems for fuzzy mappings in probabilistic metric spaces[J].Fuzzy Sets and Systems,1997,87(3):325-334
    [12] 蒋沈庆,方锦暄.Menger PM-空间中模糊映射的一个新的不动度定理[J].南京师大学报:自然科学版,2009,32(3):1-5 JIANG Shenqing,FANG Jinxuan.A new common fixed degree theorem for fuzzy mappings in Menger PM-spaces[J].Journal of Nanjing Normal University:Natural Science Edition,2009,32(3):1-5
    [13] 张石生.不动点理论及应用[M].重庆:重庆出版社,1984 ZHANG Shisheng.Fixed point theory and applications[M].Chongqing:Chongqing Publishing House,1984
    [14] 张石生.概率度量空间的基本理论及应用(Ⅱ)[J].应用数学和力学,1988,9 (3):193-204 ZHANG Shisheng.Basic theory and applications of probabilistic metric spaces (Ⅱ)[J].Applied Mathematics and Mechanics,1988,9(3):193-204
    [15] Schweizer B,Sklar A.Statistical metric spaces[J].Pacific Journal of Mathematics,1960,10(1):313-334
    [16] Schweizer B,Sklar A,Thorp E.The metrization of statistical metric spaces[J].Pacific Journal of Mathematics,1960,10(2):673-675
    引证文献
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].南京信息工程大学学报(自然科学版),2013,5(5):472-477
JIN Xin, XIAO Jianzhong. Fixed point and fixed degree theorems for nonlinear contraction in Menger spaces[J]. Journal of Nanjing University of Information Science & Technology, 2013,5(5):472-477

复制
分享
文章指标
  • 点击次数:
  • 下载次数:
  • HTML阅读次数:
  • 引用次数:
历史
  • 收稿日期:2012-10-23

地址：江苏省南京市宁六路219号    邮编：210044

联系电话：025-58731025    E-mail：nxdxb@nuist.edu.cn

南京信息工程大学学报 ® 2025 版权所有  技术支持：北京勤云科技发展有限公司