Let Sf,n and Kf,n be the functions defined in Schröder's method of the first and second kind for an entire function f with given order n (n≥2), respectively. Based on unrefined algebra characterizations of Sf,n and Kf,n, we obtain some sufficient conditions on f such that both Sf,n and Kf,n possess given finite pairs of extraneous non-repelling cycles. Here, these conditions are a pair of equations, which have infinitely many polynomials or transcendental entire functions as its solutions. For obtaining some solutions f of such equations, we ...
