Journal of Inequalities and Applications Volume 7 Issue 3

Journal Article

On unitarily invariant norms of matrix-valued linear positive operators

Stefano Serra, Capizzano; Paolo , Tilli

1900 Journal of Inequalities and Applications

In this paper we prove several inequalities concerning invariant norms of matrices belonging to the range of some matrix-valued Linear Positive Operator (LPO). We provide a variational characterization of unitarily invariant norms in terms of bilinear forms and a kind of Cauchy-Schwarz inequality...

Open Access

Journal Article

On the constants in some inequalities for the Sobolev norms and pointwise product

Carlo , Morosi; Livio , Pizzocchero

1900 Journal of Inequalities and Applications

We consider the Sobolev norms of the pointwise product of two functions, and estimate from above and below the constants appearing in two related inequalities.

Open Access

Journal Article

Existence of solutions for a class of nonlinear degenerate elliptic equations

Albo Carlos, Cavalheiro

1900 Journal of Inequalities and Applications

In this paper we prove a existence result for solution to a class of nonlinear degenerate elliptic equation associated with a class of partial differential operators of the form \(Lu(x) = \sum\limits_{i,j = 1}^n {D_j (a_{ij} (x)D_i u(x)),\,\,{\text{with}}\,D_j = \frac{\partial }{{\partial x_j }}}...

Open Access

Journal Article

Shapiro’s cyclic inequality for even n

P. J., Bushell; J. B., Mcleod

1900 Journal of Inequalities and Applications

In 1954 H. S. Shapiro proposed an inequality for a cyclic sum in $n$ variables. All the numerical evidence indicates that the inequality is true for even $n \leq 12$ and for odd $n \leq 23$. We give an analytic proof for the case $n = 12$, which implies the former result. The remaining case $n =...

Open Access

Journal Article

Asymptotic behavior inside the disk for Lebesgue Sobolev orthogonal polynomials

E. , Berriochoa; A. , Cachafeiro

1900 Journal of Inequalities and Applications

In the present paper we study the behavior, inside and on the unit disk, of the monic orthogonal polynomials with respect to the following Sobolev inner product \(\langle {f,g} \rangle _s = \int_0^{2\pi } {f(e^{i\theta } )\overline {g(e^{i\theta } )} d\mu (\theta ) + \int_0^{2\pi } {f'(e^{i\theta...

Open Access

Journal Article

Isoperimetric inequality for div-curl fields

Menita , Carozza; Antonia Passarelli, di Napoli

1900 Journal of Inequalities and Applications

Let $(E,B)$ be a Hölder conjugate pair of vector fields, both belonging to the space $L^{(2n - 2)/n} (\mathbb{R}^n ;\mathbb{R}^n )$. Suppose that div $B = 0$ and curl $E = 0$. In this paper we prove the following isoperimetric type inequality \(\int_B {J(x,\mathcal{F})dx \leq c_n \left(...

Open Access

Journal Article

On inequalities of Bohr and Bernstein

Ha Huy, Bang

1900 Journal of Inequalities and Applications

In this paper, we study inequalities of Bohr-Favard and Bernstein for $N_\Phi $-spaces generated by concave functions $\Phi $.

Open Access

Journal Article

Transfinite diameter of Bernstein sets in ℂ N

Leokadia , Bialas-Cież; Mieczysław , Jedrzejowski

1900 Journal of Inequalities and Applications

Let $K$ be a compact set in $\mathbb{C}^N $ satisfying the following generalized Bernstein inequality: for each $\alpha \in \mathbb{N}^N $ such that $|\alpha | \in \mathcal{T}$, for each polynomial $P$ of degree $|\alpha |$\(\max \left\{ {\left| {D^\alpha P(z)} \right|:z \in K} \right\} \leq...

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Journal of Inequalities and Applications Volume 7 Issue 3

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