Inequalities for linear combinations of monomials in p-Newton sequences

Bernstein-type Inequalities for Linear Combinations of Shifted Gaussians

Let Pn be the collection of all polynomials of degree at most n with real coefficients. A subtle Bernstein-type extremal problem is solved by establishing the inequality ‖U (m) n ‖Lq(R) ≤ (cm)n‖Un‖Lq(R) for all Un ∈ e Gn, q ∈ (0,∞], and m = 1, 2, . . . , where c is an absolute constant and e Gn := ( f : f(t) = N X j=1 Pmj (t)e −(t−λj )2 , λj ∈ R , Pmj ∈ Pmj , N X j=1 (mj + 1) ≤ n ) . Some relat...

Zeros of linear combinations of Laguerre polynomials from different sequences

We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely Rn = L α n + aL α n and Sn = L α n + bL α n−1. Proofs and numerical counterexamples are given in situations where the zeros of Rn, and Sn, respectively, interlace (or do not in general) with the zeros of L α k , L ′ k , k = n or n− 1. The results we prove ho...

INEQUALITIES FOR THE p-ANGULAR DISTANCE IN NORMED LINEAR SPACES

New upper and lower bounds for the p-angular distance in normed linear spaces are given. Some of the obtained upper bounds are better than the corresponding results due to L. Maligranda recently established in the paper [Simple norm inequalities, Amer. Math. Monthly, 113(2006), 256-260].

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups

Generalized Newton–like Inequalities

The notion of Newton–like inequalities is extended and an inductive approach is utilized to show that the generalized Newton–like inequalities hold on elementary symmetric functions with self–conjugate variables in the right half–plane.