On a certain functional equation in the algebra of polynomials with complex coefficients.
On a Conjecture of Sendov about the Critical Points of a Polynomial.
On a geometric property of Lemniscates.
On a geometric property of Lemniscates. (Short Communication).
On a polynomial inequality of P. Erdős and T. Grünwald.
On a Problem of Best Uniform Approximation and a Polynomial Inequality of Visser
In this paper, a generalization of a result on the uniform best approximation of α cos nx + β sin nx by trigonometric polynomials of degree less than n is considered and its relationship with a well-known polynomial inequality of C. Visser is indicated.
On growth of polynomials.
On maximum modulus for the derivative of a polynomial
If P(z) is a polynomial of degree n, having all its zeros in the disk [...] then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] that [...] In this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type [...] Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.
On Rolle's theorem for polynomials over the complex numbers.
On the behavior of algebraic polynomials in regions with piecewise smooth boundary without cusps
We continue studying the estimation of Bernstein-Walsh type for algebraic polynomials in regions with piecewise smooth boundary.
On the complexification of real-analytic polynomial mappings of ℝ²
We give a simple algebraic condition on the leading homogeneous term of a polynomial mapping from ℝ² into ℝ² which is equivalent to the fact that the complexification of this mapping can be extended to a polynomial endomorphism of ℂℙ². We also prove that this extension acts on ℂℙ²∖ℂ² as a quotient of finite Blaschke products.
On the continuity of the Faber mapping
On the extendability of quadratic polynomial mappings of the plane
We shall prove, using the result from our previous paper [Ann. Polon. Math. 88 (2006)], that for a quadratic polynomial mapping Q of ℝ² only the geometric shape of the critical set of Q determines whether the complexification of Q can be extended to an endomorphism of ℂℙ². At the end of the paper we describe some interesting classes of quadratic polynomial mappings of ℝ² and give some examples.
On the location of zeros of complex polynomials.
On the maximum modulus of a polynomial and its derivatives.
On the maximum modulus of polynomials. II.
On the minimal distance of the zeros of a polynomial.
On the paths to the zeros of a polynomial.
On the proximate order of and
On Two Functional Equations Connected with a Mean-Value Property of Polynomials