DOI: 10.2298/aadm250722030m ISSN: 1452-8630

Some properties of a linear operator defined through the Schur-Szegő composition theorem and Bernstein type inequalities

Gradimir Milovanovic, Idrees Qasim, Abdullah Mir
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In this manuscript, we investigate a linear operator Tg acting on complex polynomials, defined through the Schur-Szegő composition theorem. For this operator, we establish sharp Bernstein-type inequalities for polynomials on the unit disk. Our results not only recover several known theorems as special cases but also provide new estimates for wider classes of Bn-Operators. This work strengthens the link between operator theory and polynomial inequalities, with applications to geometric function theory and approximation theory.

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