Sharp generalized Papenfuss-Bach-type inequality

A Sharp Inequality of Ostrowski-grüss Type

The main purpose of this paper is to use a Grüss type inequality for RiemannStieltjes integrals to obtain a sharp integral inequality of Ostrowski-Grüss type for functions whose first derivative are functions of Lipschitizian type and precisely characterize the functions for which equality holds.

A Sharp Bernstein-type Inequality for Exponential Sums

A subtle Bernstein-type extremal problem is solved by establishing the equality sup 06=f∈e E2n |f ′(0)| ‖f‖[−1,1] = 2n − 1 , where e E2n := ( f : f(t) = a0 + n X j=1 aje λjt + bje −λjt , aj , bj , λj ∈ R ) . This settles a conjecture of Lorentz and others and it is surprising to be able to provide a sharp solution. It follows fairly simply from the above that 1 e − 1 n − 1 min{y − a, b − y} ≤ s...

A New Generalized Gronwall-Bellman Type Inequality

A sharp weighted Wirtinger inequality

We obtain a sharp estimate for the best constant C > 0 in the Wirtinger type inequality

The Sharp Energy-capacity Inequality

Using the Oh–Schwarz spectral invariants and some arguments of Frauenfelder, Ginzburg, and Schlenk, we show that the π1-sensitive Hofer– Zehnder capacity of any subset of a closed symplectic manifold is less than or equal to its displacement energy. This estimate is sharp, and implies some new extensions of the Non-Squeezing Theorem.