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An inequality of W.L. Wang and P.F. Wang.

International Journal of Mathematics and Mathematical Sciences

A continuous and a discrete variant of Wirtinger's inequality.

Mathematica Pannonica

A note on a functional inequality.

International Journal of Mathematics and Mathematical Sciences

On Carleman's inequality

Portugaliae mathematica

Inequalities for Weierstrass products

Portugaliae mathematica

The inequality of Milne and its converse. II.

Journal of Inequalities and Applications [electronic only]

Verschärfung einer Ungleichung von Ky Fan.

Aequationes mathematicae

An inequality for arithmetic and harmonic means.

Aequationes mathematicae

Ein Symmetrisches Mittel in Zwei Veraenderlichen

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Über einen Wert, der zwischen dem geometrischen und dem arithmetischen Mittel zweier Zahlen liegt.

Elemente der Mathematik

Ungleichungen für (e/a)a (b/e)b.

Elemente der Mathematik

Über Lehmers Mittelwertfamilie.

Elemente der Mathematik

Über eine Verallgemeinerung der Bernoullischen Ungleichung.

Elemente der Mathematik

Cyclic mean-value inequalities for the gamma function

Colloquium Mathematicae

On an inequality of Gauss.

In this note we prove a new extension and a converse of an inequality due to Gauss.

On Ozeki’s inequality for power sums

Czechoslovak Mathematical Journal

Let $p\in \left(0,1\right)$ be a real number and let $n\ge 2$ be an even integer. We determine the largest value ${c}_{n}\left(p\right)$ such that the inequality $\sum _{i=1}^{n}{|{a}_{i}|}^{p}\ge {c}_{n}\left(p\right)$ holds for all real numbers ${a}_{1},...,{a}_{n}$ which are pairwise distinct and satisfy ${min}_{i\ne j}|{a}_{i}-{a}_{j}|=1$. Our theorem completes results of Ozeki, Mitrinović-Kalajdžić, and Russell, who found the optimal value ${c}_{n}\left(p\right)$ in the case $p>0$ and $n$ odd, and in the case $p\ge 1$ and $n$ even.

A short proof of Ky Fan's inequality

Archivum Mathematicum

An inequality for the coefficients of a cosine polynomial

Commentationes Mathematicae Universitatis Carolinae

We prove: If $\frac{1}{2}+\sum _{k=1}^{n}{a}_{k}\left(n\right)cos\left(kx\right)\ge 0\phantom{\rule{4.0pt}{0ex}}\text{for}\phantom{\rule{4.0pt}{0ex}}\text{all}\phantom{\rule{4.0pt}{0ex}}x\in \left[0,2\pi \right),$ then $1-{a}_{k}\left(n\right)\ge \frac{1}{2}\frac{{k}^{2}}{{n}^{2}}\phantom{\rule{4.0pt}{0ex}}\text{for}\phantom{\rule{4.0pt}{0ex}}k=1,\cdots ,n.$ The constant $1/2$ is the best possible.

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