Functions with constant sums over a hyperplane and applications

Abstract

Two functional equations exhibiting functions with constant sums over points lying in a hyperplane are solved, and the results are applied to characterize major trigonometric and hyperbolic functions.

Characterizing Hyperbolic Functions over a Hyperplane

“…where A 3 is an additive function on R, and the constants t j satisfy ∑ n j=1 t j = 0. In passing, let us remark that characterizations along the same vein as above for the trigonometric sine and cosine functions have already been carried out in [5].…”