| Orthogonality is an important property of Euclidean space and an important research direction in normed space,ρ-orthogonality plays an important role in the orthogonality of normed space.A 2-normed space is a generalization of normed space.Geometrically,2-norm is the area of a parallelogram spanned by two related vectors.In this paper,we mainly study the ρ-orthogonality properties in 2-normed space.In the first chapter,we first introduce the research progress of ρ-orthogonality in normed space,and give the relationship between ρ-orthogonality and other orthogonality in normed space.Secondly,we introduce the definition and properties of 2-normed space,2-inner product space,2-semi-inner product space,and the research progress of orthogonality properties in these spaces.In the second chapter,we first introduce the properties of 2-norm derivative in 2-normed space.The ρ-orthogonality property in 2-normed space is given by the 2-norm derivative.Secondly,the properties of 2-norm derivative in 2-inner product space and 2-semi-inner product space are discussed.Finally,the relationship between b-orthogonality and 2-norm derivative in 2-normed space is given.In the third chapter,we give the definition of ρ-orthogonality,ρ+-orthogonality and ρ--orthogonality in 2-normed space,and study the relationship between the three orthogonalities and the properties of ρ-orthogonality. |
