Abstract. A function
s(x,y) = inf { ||x + λ y|| / ||x|| : λ ∈ R }
strictly connected with Birkhoff-James orthogonality is considered. This function may be used in functional equations theory, to provide unconditional equations in place of orthogonal equations in the sense of Birkhoff-James. Moreover, we deal with another generalization of the sine function which, in particular leads to a characterization of inner product spaces.2000 Mathematics Subject Classification. 39B52, 46B20.
Key words and phrases. Birkhoff-James orthogonality, functional equation, inner product space.