Results 61 to 65 of about 551,551 (65)

The inequality of Ky Fan and related results

Acta Applicandae Mathematicae, 1995
This survey paper presents refinements, extensions, and variants of the well-known Ky Fan inequality \[ \prod^n_{i = 1} \bigl( y_i/(1 - y_i) \bigr)^{1/n} < \sum^n_{i = 1} y_i \left/ \sum^n_{i = 1} \right. (1 - y_i), \] valid for all real numbers \(y_i \in (0,1/2]\) \((i = 1, \ldots, n)\) which are not all equal.
openaire   +1 more source

Ky Fan's inequality via convexity

2008
Summary: Using the strict convexity and concavity of the function \( f(x)=\frac{1}{1+e^x}\) on \( [0,\infty)\) and \( (-\infty,0]\) respectively, we prove Ky Fan's inequality by separating the left and right hands of it by \( \frac{1}{G_n+G^{\prime }_n}\).
openaire   +1 more source

The isoperimetric inequality for the Ky Fan norm

We show that, among all measurable sets $Ω\subset \mathbb{C}$ with finite area $s$, the disc of area $s$ maximizes the Ky Fan norm, which is defined as the sum of the first $N$ eigenvalues of the Toeplitz operator with symbol $\mathbf{1}_{Ω}$ on the Fock space. For $N=1$ this reduces to Nicola-Tilli's celebrated Faber--Krahn inequality and for general $
openaire   +1 more source

On Linear Inequalities (Moment Inequalities) and Some Results of Ky Fan

Mathematische Nachrichten, 1974
openaire   +1 more source

AN EXTENSION AND A CONVERSE OF KY FAN'S INEQUALITY

Quaestiones Mathematicae, 1990
openaire   +1 more source