On Two Functional Equations

Ganapathy Iyer ([3], [4]) has discussed the solutions of the functional equations

f(z + A) = g(z)f(z)----(1)
f(λz) = g(z)f(z)-------(2)

where f and g are meromorphic functions. Recently Fred Gross ([2]) has proved that any pair of nonconstant entire functions f, g satisfying equations (1) and (2) cannot both have only at most a finite number of fix-points.