Recent work by Lau and Yao (J Math Anal Appl 459:203–216, 2018) and Mohamadi (J Fixed Point Theory Appl 21:83, 2019) initiated the study of common fixed points for commuting families of multivalued mappings. Working in locally convex linear spaces the authors assumed that the mappings are convex with the exception that Mohamadi established a common fixed point result for non-convex mappings in one-dimensional Euclidean space. Our purpose is to advance their work by giving common fixed point results for non- convex commuting multivalued mappings in metric trees. Our main conclusion states that in a complete geodesically bounded metric tree a family of nonexpansive commuting multivalued mappings with closed, bounded and convex values has a common fixed point.

Lau 和 Yao (J Math Anal Appl 459:203–216, 2018) 和 Mohamadi (J Fixed Point Theory Appl 21:83, 2019) 最近的工作启动了对多值映射通勤族的公共不动点的研究。在局部凸线性空间中，作者假设映射是凸的，除了 Mohamadi 为一维欧几里德空间中的非凸映射建立了一个公共不动点结果。我们的目的是通过为度量树中的非凸交换多值映射提供公共不动点结果来推进他们的工作。我们的主要结论指出，在完整的测地界度量树中，具有闭、有界和凸值的非扩展交换多值映射族具有公共不动点。