The Minkowski Plane Generalized Orthogonal And Geometric Constants D (x) Study

The concept of orthogonality plays a very important role in Euclidean geometry. In the research of the geometry of normed linear spaces a potential topic is to look for a new concept in a more general space to replace the orthogonality in Euclidean space. Generalized orthogonality types in normed spaces are the generalization of orthogonality types in inner product spaces. A large number of fundamental results have been obtained by several researchers working on generalized orthogonality types and the relationship among them, mainly focusing on the discussion of these gener-alized orthogonalities and their influence on the global spaces. And few was done on the pointwise properties of generalized orthogonality types. On the other hand, the known results on the relationship between different orthogonality types are mostly qualitative. The quantitative characterizations are just carried out recently.First, this paper introduce several concepts and properties of Minkowski space, generalized orthogonalities, and D(X).Secondly, we get some new conclusion of the relationship generalized orthogo-nality types.Thirdly, Singer orthogonality are discussed. It is proved that some Singer or-thogonality inherits certain properties isosceles orthogonality. In addition, some charaterizations of Singer orthogonality, Birkhoff orthogonality and inner product spaces are obtained.In the end, we prove a property of Orlicz function M(u), and get some properties of Orlicz space as well as compute D(X) of Orlicz space.