| In this paper, we shall introduce a new geometric constant R_X(κ) based on isosceles
orthogonality. First, we investigate some basic properties of the new constant, a few examples to
estimate the exact values of this constant in some specific Banach spaces are then given. Next,
the relations between the R_X(κ) constant and other classical constants are studied, specifically, an
inequality relationship between the R_X(κ) constant and the J(X) constant as well as an identity
of the R_X(κ) constant and the ρ_X(t) constant are established. Furthermore, some geometric
properties of Banach spaces are characterized in terms of the RX(κ) constant. Finally, restricting
the above R_X(κ) constant to the unit sphere, we shall introduce another new constant R'_X(κ).
The upper and lower bounds of this new constant are calculated and an example is given. |
