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We introduce the metric space valued in partially ordered groups, and definethe convergence of sequences and the multi-valued weak contractions, etc., onthe space. We then establish endpoint theorems for the defined maps. Ourcontributions extend the theory of cone metric space constructed by Huang andZhang (2007) and some recent results on the fixed point and endpoint theory,such as the endpoint theorem given by Amini-Harandi (2010).

Endpoints of multi-valued weak contractions on the metric space valued in partially ordered groups