单调偏序模度量空间上收缩多值映射的端点（英文）

Endpoints for contractive multi-valued maps on the metric space of partially ordered module with monotonic laws

不动点理论是一个十分有趣和有益的问题,有着广泛的的应用价值与深刻的理论价值。该领域主要研究各种空间中的各种映射的不动点的存在性、唯一性及其求解方法。端点问题是不动点理论中的一项新的研究内容。Huang和Zhang于2007年首次引入锥度量空间,并研究其上的压缩映射的不动点问题,发展了几个不动点定理。近年来,发展各种空间并研究其上各种映射的不动点问题激发了许多学者的热情。引入关于具有单调律的偏序模的度量空间与相关序列收敛性,扩展了Huang和Zhang于2007年引入的锥度量空间与相关序列的收敛性;建立了3个关于该空间上的收缩多值映射的端点定理。这些研究不仅丰富了不动点领域的研究内容与研究深度,还促进了分析学与代数学的互相融和。

The problem of endpoints is a new study line of the fixed point theory.The fixed point theory is very interesting and meaningful,which has a wide range of applications and profound theoretical value.The research area mainly studies the existence,uniqueness and solution method of fixed points of various mappings in different spaces.In 2007,Huang and Zhang introduced cone metrics paces,proved some fixed point theorems of contractive mappings on cone metric spaces.In recent years,the problem of developing different spaces and researching fixed points of various mappings in the developed spaces excited research enthusiasm of many scholars.In this paper we develop the metric space of partially ordered module with monotonic laws and the related convergence of sequences,which extend the cone metric space and the related convergence of sequences introduced by Huang and Zhang(2007).And establish three endpoint theorems for contractive multi-valued maps on such space,which cover some recent results of the fixed point theory.Our contributions not only vastly extend the range and the depth of the fixed point research area,but also strongly advance the mutual influences between the analysis and algebra.