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We will introduce four new geometric constants closely related to the James constant J (X) , which have symmetric structure, along with a discussion on the relationships among them and some other well-known geometric constants via several inequalities, together with the calculation of several values on some specific spaces. In addition, we will characterize geometric properties of J 1 (X) , such as uniform non-squareness and uniformly normal structure. [ABSTRACT FROM AUTHOR]

We will introduce some new geometric constants based on the constant H (X) proposed by Gao and the constant A 2 (X) proposed by M. Baronti et al. We first provide a study of a new constant M 1 (X) closely related to the midlines of equilateral triangles, including a discussion of some of its properties and the connections with other parameters of the sphere. Next, we focus on a new constant M 2 (X) and its generalized form M 2 (X , p , q) , along with some of their basic properties. Finally, we concentrate on a new constant M 3 (X) and discuss some of its properties. [ABSTRACT FROM AUTHOR]