Julia sets of two permutable entire functions

In this paper first we prove that if f and g are two permutable transcendental entire functions satisfying f = f(1) (h) and g = g(1) (h), for some transcendental entire function h, rational function f(1) and a function g(1), which is analytic in the range of h, then F(g) subset of F(f). Then as an application of this result, we show that if f(z) = p(z)e(q(z)) + c, where c is a constant, p a nonzero polynomial and q a nonconstant polynomial, or f(z) = integral(z) p(z)e(q(z)) dz, where p, q are nonconstant polynomials, such that f(g) = g(f) for a nonconstant entire function g, then J(f) = J(g)