Abstract
To describe the geometry of normed space, many geometric constants have been investigated. Among them, the von Neumann–Jordan constant has been treated by a lot of mathematicians. Here we also consider Birkhoff orthogonality and isosceles orthogonality. The usual orthogonality in inner product spaces and isosceles orthogonality in normed spaces are symmetric. However, Birkhoff orthogonality is not symmetric in general normed spaces. A two-dimensional normed space in which Birkhoff orthogonality is symmetric is called Radon plane. We consider the upper bound of a geometric constant in Radon planes. Then we estimate the von Neumann–Jordan constant in Radon planes.
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