Abdeljawad, Thabet2016-06-272025-09-182016-06-272025-09-182011Abdeljawad, T. (2011). Order norm completions of cone metric spaces. Numerical Functional Analysis and Optimization, 32(5), 477-495. http://dx.doi.org/10.1080/01630563.2011.5638920163-05631532-2467https://doi.org/10.1080/01630563.2011.563892https://hdl.handle.net/20.500.12416/10418Abdeljawad, Thabet/0000-0002-8889-3768In this article, a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved. The completion spaces are constructed by means of an equivalence relation defined via an ordered cone norm on the Banach space E whose cone is strongly minihedral and ordered closed. This order norm has to satisfy the generalized absolute value property. In particular, if E is a Dedekind complete Banach lattice, then, together with its absolute value norm, satisfy the desired properties.eninfo:eu-repo/semantics/closedAccessAbsolute Value PropertyCone BanachCone IsometryCone MetricStrongly MinihedralUniformly ContinuousArticle10.1080/01630563.2011.5638922-s2.0-79953681618