Stechkin–Marchaud-Type Inequalities for Baskakov Polynomials

Markov-type Inequalities for Constrained Polynomials

On Lojasiewicz-Type Inequalities for Exponential Polynomials

where fi, . . . . f, are exponential polynomials of n variables. One such example is the work of Symes on materials testing [ZS]. The authors have given other examples in [6,7, 10, 31 J. The kind of bounds we have in mind are the following. Let Y= {ZEC’? f,(z)= .” =f,(z)=O} and let p(z) be a weight function (see definition below), then we would like to show the existence of positive constants A...

Inequalities of Rafalson type for algebraic polynomials

For a positive Borel measure dμ, we prove that the constant γn(dν; dμ) := sup π∈Pn\{0} ∫∞ −∞ π (x)dν(x) ∫∞ −∞ π 2(x)dμ(x) , can be represented by the zeros of orthogonal polynomials corresponding to dμ in case (i) dν(x) = (A + Bx)dμ(x), where A + Bx is nonnegative on the support of dμ and (ii) dν(x) = (A + Bx)dμ(x), where dμ is symmetric and A + Bx is nonnegative on the support of dμ. The extre...

Markov-bernstein Type Inequalities for Polynomials under Erdős-type Constraints

Throughout his life Erdős showed a particular fascination with inequalities for constrained polynomials. One of his favorite type of polynomial inequalities was Markovand Bernstein-type inequalities. For Erdős, Markovand Bernstein-type inequalities had their own intrinsic interest. He liked to see what happened when the polynomials are restricted in certain ways. Markovand Bernstein-type inequa...

Some compact generalization of inequalities for polynomials with prescribed zeros

‎Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$‎, ‎$k^2 leq rRleq R^2$ and for $Rleq r leq k$‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.