The purpose of this paper is to give a new method of finding the solution of Lobashevsky's functional equation and those of other classical functional equations. At the beginning we present the properties of solution $f, \; f \neq 0$, of Lobachevsky's functional equation. Using only the boundedness property on $(-r, r)$, we deduce the continuity, convexity and differentiability properties of the solution.
Neamtu, Nicolae (1998) "About Some Classical Functional Equations," Turkish Journal of Mathematics: Vol. 22: No. 1, Article 12. Available at: https://journals.tubitak.gov.tr/math/vol22/iss1/12