On the equivalent p-th von Neumann-Jordan constant associated with isosceles orthogonality in Banach spaces

Abstract: In this paper, we define a new geometric constant based on isosceles orthogonality, denoted by . Through research, we find that this constant is the equivalent p-th von Neumann Jordan constant in the sense of isosceles orthogonality. First, we obtain some basic properties of the constant. Then, we calculate the upper and lower bounds of the constant. Through three examples, it is found that the upper bound of the constant is attainable. We also compare the relationship between this constant and other constants. Finally, we establish the connection between the constant and some geometric properties in Banach spaces, such as uniform non-squareness, uniform smoothness.