The zeros on complex differential-difference polynomials of certain types

In this paper, we consider the zeros distribution of \(f(z)P(z,f) -q(z)\), where \(P(z,f)\) is a linear differential-difference polynomial of a finite-order transcendental entire function \(f(z)\), and \(q(z)\) is a nonzero polynomial. To a certain extent, Theorem 1.1 generalizes the recent results (Latreuch and Belaidi in Arab. J. Math. 7(1):27–37, 2018; Lu et al. in Kodai Math. J. 39(3):500–509, 2016) related to Hayman conjecture (Hayamn in Ann. Math. 70:9–42, 1959).