完全度量空间中余循环映射与子循环映射的公共不动点
Common Fixed Points of Co-Cyclic and Sub-Cyclic Mappings in Complete Metric Spaces
AI总结：
本文在完全度量空间中引入余循环与子循环映射，在Jungck型压缩条件和相容性假设下证明其唯一公共不动点定理，并给出例子及开放问题。
AI中文摘要：
本文在度量空间的两个子集的并集上引入了两类新的循环型映射，即余循环映射和子循环映射。在适当的Jungck型压缩条件和相容性假设下，我们在完全度量空间中为这些映射建立了唯一的公共不动点定理。证明基于适当序列的构造、相关的压缩条件以及底层度量空间的完备性。文中提供了例子来说明所提出的概念并展示主要结果的可适用性。最后，提出了关于余循环映射和子循环映射的一些开放问题及进一步研究的可能方向。
英文摘要：
In this paper, we introduce two new classes of cyclic-type mappings, namely, co-cyclic mappings and sub-cyclic mappings, defined on the union of two subsets of a metric space. Under suitable Jungck-type contractive conditions and compatibility assumptions, we establish unique common fixed point theorems for these mappings in complete metric spaces. The proofs are based on the construction of appropriate sequences, the associated contractive conditions, and the completeness of the underlying metric space. Examples are provided to illustrate the proposed concepts and to demonstrate the applicability of the main results. Finally, some open questions and possible directions for further research concerning co-cyclic and sub-cyclic mappings are presented.
