inequalities for an operator on the space of polynomials

Let pn be the class of all complex polynomials of degree at most n. recently rather et. al.[on the zeros of certain composite polynomials and an operator preserving inequalities, ramanujan j., 54(2021) 605–612. https://doi.org/10.1007/s11139-020-00261-2] introduced an operator n : pn → pn defined by n[p](z) := σk j=0 λj (nz/2)j p(j) (z)/j!, k ≤ n where λj ∈ c, j = 0, 1, 2, . . . , k are such that all the zeros of φ(z) = σk j=0 (nj) λj zj lie in the half plane |z| ≤ |z-n/2| and established certain sharp bernstein-type polynomial inequalities. in this paper, we prove some more general results concerning the operator n : pn → pn preserving inequalities between polynomials. our results not only contain several well known results as special cases but also yield certain new interesting results as special cases.