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Let Pn be the class of polynomials of degree at most n . In 1969, Rahman [Functions of exponential type, Trans. Amer. Math. Soc., 135(1969), 295-309] introduced a class Bn of operators B that map Pn into itself and proved that max |z|=1 ∣∣B[P(Rz)] ∣∣ ∣∣B[En(Rz)] ∣∣max |z|=1 |P(z)|, R 1, for every B ∈ Bn , where En(z) := zn . In this paper, we prove some generalizations and refinements of this result, which in particular yields some known polynomial inequalities as special cases. Mathematics subject classification (2010): 30A10, 30C10, 30C15.

Generalizations of some polynomial inequalities for the family of B-operators