Geometry of orthogonality using angular distance function in normed spaces

Abstract

This work introduces an angular function orthogonality based on the angular distance function in normed spaces.
We examine the geometrical features of the aforementioned orthogonality by discussing its homogeneity, alpha-existence, and the conditions under which it may exhibit symmetry.
Motivated by the stated orthogonality, we introduce a well-defined angle using the angular distance function and discuss its geometrical properties by defining acute, obtuse, and right angles in normed spaces. Some non-trivial examples are also provided to support the results. Furthermore, we discuss the relationship of the angle with the Euclidean, isosceles, and Thy angles.