On two functional equations originating from number theory

摘要

Reducing the functional equations introduced in Proc. Indian Acad. Sci. (Math. Sci.) 113(2) (2003) 91a€“98 and in Appl. Math. Lett. 21 (2008) 974a€“977 to equations in complex variables and quaternions, we find general solutions of the equations. We also obtain the stability of the equations.