Let P(z):= ?n v=0 avzv be a univariate complex coefficient polynomial of degree n. Then as generalization well-known classical inequality Tur?n [25], it was shown by Govil [7] that if P(z) has all its zeros in |z| ? k, k 1, then max |z|=1 |P?(z)| n/1 + kn |P(z)|, whereas, , 0 < again [6] who gave an extension the Erd?s-Lax [13], obtaining provided and |Q?(z)| attain maximum at same point on ...

We establish various inequalities relating the coefficients of a polynomial with the separation of its roots. Applications are given to oscillatory integrals and sublevel sets in euclidean harmonic analysis as well as exponential sums and polynomial congruences in number theory. These applications depend on precise structural statements of sublevel sets for polynomials with coefficients in a ge...

Recently Cherchye et al. (2011) reformulated the Walrasian equilibrium inequalities, introduced by Brown and Matzkin (1996), as an integer programming problem and proved that solving the Walrasian equilibrium inequalities is NPhard. Brown and Shannon (2002) derived an equivalent system of equilibrium inequalities ,i.e., the dual Walrasian equilibrium inequalities. That is, the Walrasian equilib...

Some new properties of kernels of modified Kontorovitch–Lebedev integral transforms — modified Bessel functions of the second kind with complex orderK 1 2+iβ (x) are presented. Inequalities giving estimations for these functions with argument x and parameter β are obtained. The polynomial approximations of these functions as a solutions of linear differential equations with polynomial coefficie...

This is a survey of some recent results concerning polynomial inequalities and polynomial approximation of functions in the complex plane. The results are achieved by the application of methods and techniques of modern geometric function theory and potential theory. MSC: 30C10, 30C15, 41A10

This paper shows how the solutions of constraint satisfaction problems that involve only polynomial constraints over finite domains can be enumerated by computing the values of related polynomial functions at appropriate points. The proposed algorithm first transforms constraints, which are expressed as equalities, inequalities, and disequalities of polynomials with integer coefficients and int...

In this paper, we generalize the classical Bonferroni inequalities and their improvements by Galambos to sums of type ∑ I⊆U (−1)|I|f(I) where U is a finite set and f : 2 → R. The result is applied to the Tutte polynomial of a matroid and the chromatic polynomial of a graph.

We show that, for fixed dimension n, the approximation of inner and outer j-radii of polytopes in N", endowed with the Euclidean norm, is in P. Our method is based on the standard polynomial time algorithms for solving a system of polynomial inequalities over the reals in fixed dimension.