Under consideration are the well-known extremal problems of Bernstein-type which relate
the uniform norm between polynomials on the unit disk in the plane. We establish a few new …

If P (z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β∈ C
with∣ α∣⩽ 1,∣ β∣⩽ 1, it is known that. for R⩾ 1 and∣ z∣⩾ 1. The present paper contains …

Generalization of Certain Inequalities for a Polynomial and Its Derivative1 Page 1 ISSN
1995-0802, Lobachevskii Journal of Mathematics, 2012, Vol. 33, No. 1, pp. 68–74. c © Pleiades …

For a rational function r (z) having no zeros outside a unit disk, Li et al.(J Lond Math Soc 51:
523–531, 1995) proved:| r′(z)|≥| B′(z)|| r (z)|, for| z|= 1, where B (z) is the Blashke …

Some Generalization for an Operator Which Preserving Inequalities Between Polynomials 1
Introduction and statement of results Page 1 Analysis in Theory and Applications Anal. Theory …

Рассматриваются известные экстремальные задачи типа Бернштейна относительно
равномерных норм полиномов в единичном круге на плоскости. Доказаны новые …

Some Compact Generalizations of Certain Well Known Inequalities for Polynomials Page 1
Southeast Asian Bulletin of Mathematics c⃝ SEAMS. 2013 Southeast Asian Bulletin of …

This paper deals with the problem of finding some upper bound estimates for the maximal
modulus of the polar derivative of a complex polynomial on a disk under certain constraints …

Let Q (z) be a polynomial of degree n having all its zeros in| z|≤ k, k≤ 1 and p (z) be a
polynomial of degree not exceeding that of Q (z) such that| p (z)|≤| Q (z)| for| z|= k. In this …

(󵄩󵄩󵄩󵄩[𝑅𝑛− 𝛼𝑟𝑛+ 𝛽 {((𝑅+ 1)/(𝑟+ 1)) 𝑛−| 𝛼|}] 𝑧+[1− 𝛼+ 𝛽 {((𝑅+ 1)/(𝑟+ 1)) 𝑛−| 𝛼|}]󵄩󵄩󵄩󵄩 𝑝/‖ 1+ 𝑧‖
𝑝)‖ 𝑃 (𝑧)‖ 𝑝. In this paper, we will prove a result which not only generalizes the above …