非阿基米德Menger概率2-度量空间中自映射的不动点问题研究  

Study on Fixed Point Problems of Self-mappings in Non-Archimedean Menger Probabilistic 2-metric Spaces

作　　者：徐文清[1] 朱传喜[1] 吴照奇[1] 

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《工程数学学报》2015年第3期432-444,共13页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11361042;11326099);江西省自然科学基金(20132BAB201001;20142BAB211016);江西省教育厅青年基金(GJJ13012)~~

摘　　要：本文首先引入了Menger概率2-度量空间中的广义阿基米德三角范数以及非阿基米德Menger概率2-度量空间的定义,并给出了广义阿基米德三角范数的一个等价刻画.在此基础上,利用迭代方法,研究了非阿基米德Menger概率2-度量空间中满足不同类型压缩条件的自映射或自映射族的不动点或公共不动点的存在唯一性问题,得到了若干新的结果,改进和推广了之前文献中的相关结果.In this paper, we introduce the generalized Archimedean triangular norm in Menger probabilistic 2-metric spaces and Non-Archimedean probabilistic 2-metric spaces, and present a characterization of the generalized Archimedean triangular norm. Based on this, and utiliz- ing the iterative method, we investigate the existence and uniqueness of the fixed points for self-mappings or common fixed points for a family of self-mappings under various contractive conditions in Non-Archimedean probabilistic 2-metric spaces. Many new results are obtained, which extend and generalize corresponding results in the literature.

关 键 词：Menger概率2-度量空间 不动点 G-函数 阿基米德t-范数 

分 类 号：O177.91[理学—数学] O211.3[理学—基础数学]