A Cantor regular set which does not have Markov's property
A conjecture of Schoenberg.
A counterexample to the strong real Jocobian conjecture.
A criterion for unimodality.
A factored form of complex analytic functions and its application to finding partial fraction decompositions.
A factorisation of the Askey’s characteristic function
A functioanl identity characterizing polynomials.
A generalization of the Gauss-Lucas theorem
Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.
A new look at Newton's inequalities.
A new proof of a theorem about generalized orthogonal polynomials.
A note on Babylonian square-root algorithm and related variants.
A note on integration of rational functions
Let and be polynomials in one variable with complex coefficients and let be a natural number. Suppose that is not constant and has only simple roots. Then there is a rational function with if and only if the Wronskian of the functions is divisible by .
A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix
It is shown that if A is a bounded linear operator on a complex Hilbert space, then , where w(A) and ||A|| are the numerical radius and the usual operator norm of A, respectively. An application of this inequality is given to obtain a new estimate for the numerical radius of the Frobenius companion matrix. Bounds for the zeros of polynomials are also given.
A polynomial inequality generalising an integer inequality.
A pseudo Laguerre method
A Remark on the Multidimensional Moment Problem.
A simple proof of the Fundamental Theorem of Algebra
In the paper an elementary and simple proof of the Fundamental Theorem of Algebra is given.
A Unified Approach to Methods for the Simultaneous Computation of All Zeros of Generalized Polynomials.
Abschätzung der Teilsummen reeller Polynome.
Algoritmy na výpočet kořenů polynomu