Inequalities for the polar derivative of a polynomial

Some remarks on rotation theorems for complex polynomials

“…which is equivalent to (10) for z 0 = 1. If now P (z) has the form (11), then f (z) ≡ z. In this case, f ′ (1) = 1 and…”

“…Earlier [2], a weakened version of inequality (4) was established, in which the right-hand side of ( 4) is replaced by the quantity Theorem 4]. At present, the application of the boundary Schwarz lemma to inequalities for complex polynomials had raised considerable interest (see, for example, [11], [12], [14], [18] - [23], [25] and references therein ). As regards inequality (4) directly, we note the following results.…”

“…In the papers of Govil, Kumar [10] and Rather, Dar, Iqbal [19] inequality (4) is generalized in different directions and another proofs of the above inequality are given. Gulzar, Zargar, Akhter [11], Hussain, Ahmad [12], and Milovanović, Mir, and Ahmad [18] used (4) to generalize and strengthen the well-known inequalities for polynomials. In the paper of Rather, Dar, Iqbal [20] the weakened version (4) was used.…”