Skew geometric mean constants in Banach spaces

Abstract

In this paper, a new skew geometric mean constant is introduced first, and then another new constant is introduced after restricting the isosceles orthogonal condition. These constants are used to characterize Hilbert spaces. Some basic properties of these constants in Banach spaces are derived, and the values of constants in specific spaces are calculated. On this basis, the relationship between the new geometric constants and other famous constants is studied. Finally, based on these identities, the relationship between the new geometric constants and the geometrical properties in Banach spaces is discussed, such as uniform non-square and normal structure.