Local Approximate Symmetry of Birkhoff–James Orthogonality in Normed Linear Spaces

Two different notions of approximate Birkhoff–James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieliński. In the present paper we consider a global local symmetry related to each two definitions. We prove that considered is approximately symmetric sense all finite-dimensional Banach spaces. For other case, for polyhedral spaces, equivalent some newly geometric property. Our investigations complement extend scope recent results on orthogonality.