半序概率度量空间中压缩条件下相容映射的三元重合点与三元不动点定理

Tripled Coincidence and Tripled Fixed Point Theorems for Compatible Mappings Under Contractive Conditions in Partially Ordered Probabilistic Metric Spaces

在半序概率度量空间中建立了映射对G:X×X×X→X与g:X→X的相容性概念.在不需要可交换的条件下,研究了相容映射在满足更一般的非线性压缩条件下的三元重合点与三元不动点问题,所得结果推广了已有文献中的二元重合点与二元公共不动点定理.最后,给出主要结果的一个具体应用.

In this paper, we establish the notion of compatibility for a pair of mappings G：X×X×X→X and g ： X →X in partially ordered probabilistic metric spaces. Under not necessary commutative conditions, some tripled coincidence and tripled common fixed point problems of compatible mappings satisfying a more general nonlinear contractive condition are studied. The obtained results generalize some coupled common fixed point theorems in the corresponding literatures. Finally, an example is given to illustrate our main results.