Author(s)

Congdian Cheng

School of Intelligence Technology, Geely University of China, Chengdu, China.

The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively; and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).

Fixed Point, Endpoint, Metric Space Valued in Partially Ordered Group, Topological Structure, Weak Contraction

Cheng, C. (2022) Endpoints of Multi-Valued Weak Contractions on the Metric Space of Partially Ordered Groups. Advances in Pure Mathematics, 12, 638-651. doi: 10.4236/apm.2022.1211049.