基于非线性压缩的Menger空间上不动点与不动度定理

Fixed point and fixed degree theorems for nonlinear contraction in Menger spaces

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.

In this paper,we discuss the nonlinear operators in Menger probability metric spaces. We prove the ex- istence 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 estab- lish a new fixed degree theorem for fuzzy mapping.