This paper gives a survey of classical and modern theorems on polynomials, proved using
methods of geometric function theory. Most of the paper is devoted to results of the author …

Неравенства для полиномов и их производных имеют богатую историю и
многочисленные приложения (см., например,[1]-[6]). Вместе с тем применение методов …

Some applications of Dubinin's lemma to rational functions with prescribed poles -
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Let, and as a consquence of this result, we present a generalization of a theorem of O'Hara
and Rodriguez for self-inversive polynomials. Finally, we establish a similar result when …

By using a boundary refinement of the classical Schwarz lemma some results for the rational
functions with prescribed poles and restricted zeros have been proved. The estimates …

Using classical properties of conformal maps, we get new exact inequalities for rational
functions with prescribed poles. In particular, we prove a new Bernstein-type inequality, an …

Let Rn be the set of all rational function of the type r (z)= p (z)/W (z), where p (z) be a
polynomial of degree not exceeding n and let where| aj|> 1, j= 1, 2,…, n. If r, s=∊ Rn and s …

Sharp Inequalities for Rational Functions on a Circle | Mathematical Notes Skip to main
content SpringerLink Account Menu Find a journal Publish with us Search Cart 1.Home 2.Mathematical …

For rational functions, where is a polynomial of degree at the most and, with we use simple
but elegant techniques to strengthen generalizations of certain results which extend some …

In this paper, we establish some inequalities for rational functions with prescribed poles
having t-fold zeros at the origin. The estimates obtained generalise as well as refine some …