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 …

Applicable Analysis and Discrete Mathematics COMPARISON INEQUALITIES OF
BERNSTEIN-TYPE BETWEEN POLYNOMIALS WITH RESTRICTED ZEROS Page 1 Applicable …

The goal of this paper is to obtain some comparison inequalities for a linear operator
between polynomials in the plane. The polynomials under study have constraints on their …

arXiv:2411.19821v1 [math.FA] 29 Nov 2024 On operators preserving inequalities between
polynomials Page 1 arXiv:2411.19821v1 [math.FA] 29 Nov 2024 On operators preserving …

Let denote the space of all complex polynomials of degree at most. For any complex
number, denote the polar derivative of the polynomial with respect to and denote a family of …

In this paper, we establish some operator preserving inequalities of Bernstein-type in the
uniform-norm between univariate complex coefficient polynomials while taking into account …

Let P n be the class of all complex polynomials of degree at most n, and let T: P n→ P n be a
linear operator. We shall say that T is a B n-operator if for every P∈ P n having all zeros in …

In this paper, we combine the operators N and D α, and investigate the dependence of N [D
α (P (R z)-β P (rz)] on the maximum modulus of P (z) on| z|= 1 for every real or complex …

Bernstein-type inequalities play a very important role in the theory of approximation. During
last few decades, a number of operators have been identified, which preserve such type of …

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