A Hankel operator $\mathbf{H}_\varphi$ on the Hardy space $H^2$ of unit circle with analytic symbol $\varphi$ has minimal norm if $\|\mathbf{H}_\varphi\|=\|\varphi \|_2$ and maximal $\|\mathbf{H}_\varphi\| = \|\varphi\|_\infty$. The both only $|\varphi|$ is constant almost everywhere or, equivalently, a multiple an inner function. We show that norm-attaining norm, then norm. If continuous but n...

Based on the results obtained in [Hucht, J. Phys. A: Math. Theor. 50, 065201 (2017)], we show that partition function of anisotropic square lattice Ising model $L \times M$ rectangle, with open boundary conditions both directions, is given by determinant a $M/2 M/2$ Hankel matrix, equivalently can be written as Pfaffian skew-symmetric $M Toeplitz matrix. The $M-1$ independent matrix elements ma...

In a recent paper by Hirzallah et al. [O. Hirzallah, F. Kittaneh, M. Krnić, N. Lovričević, and J. Pečarić. Eigenvalue inequalities for differences of means of Hilbert space operators. Linear Algebra and its Applications, 436:1516–1527, 2012.], several eigenvalue inequalities are obtained for the difference of weighted arithmetic and weighted geometric means of two positive invertible operators ...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

We use Turán type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence pk+1 = xpk − ckpk−1, with a nondecreasing sequence {ck}. As a special case they include a non-asymptotic version of Máté, Nevai and Tot...

We show that the integrality gap of the standard SDP for VERTEX COVER on instances of n vertices remains 2− o(1) even after the addition of all hypermetric inequalities. Our lower bound requires new insights into the structure of SDP solutions behaving like l1 metric spaces when one point is removed. We also show that the addition of all l1 inequalities eliminates any solutions that are not con...

In a recent paper by Hirzallah et al. [O. Hirzallah, F. Kittaneh, M. Krnić, N. Lovričević, and J. Pečarić. Eigenvalue inequalities for differences of means of Hilbert space operators. Linear Algebra and its Applications, 436:1516–1527, 2012.], several eigenvalue inequalities are obtained for the difference of weighted arithmetic and weighted geometric means of two positive invertible operators ...

In this paper, we give an upper bound of Hankel determinant (H2(1)) for the classes M(?), ? C. Also, obtain a sharp estimate classical Fekete-Szeg? inequality. That is, will get H2(1) = c3 c22. Moreover, in class analytic functions on unit disc, assuming existence angular limit boundary point, estimations below modulus derivative have been obtained.

Let $\mathcal{S}^{\ast}_{L}(\lambda)$ be the class of functions $f$, analytic in unit disc $\Delta=\{z:|z|<1\}$, with normalization $f(0)=f'(0)-1=0$, which satisfy condition\begin{equation*}\frac{zf'(z)}{f(z)}\prec \left(1+z\right)^{\lambda},\end{equation*}where $\prec$ is subordination relation. The a subfamily known strongly starlike order $\lambda$. In this paper,the relations between and...