Zakład Optymalizacji i Sterowania: 2015-06-02 Nonlinear Seminar

Prof. Xiao-Xiong Gan
(Mathematics Department, Morgan State University, Baltimore, USA)
Some Remarks on Minkowski's Inequality

The classical Minkowski's inequality has two different forms based on the values of the positive number $p$ :

If $1 \leq p < \infty$ , then $\|f + g \|_p \leq \|f\|_p + \|g\|_p$ ;
If $0 < p < 1$ , then $\|f + g \|_p \geq \|f\|_p + \|g\|_p$ .

We provide a one-form Minkowski's inequality for all $p > 0$ . A non-conjugate Hölder's inequality is also introduced. Some applications of the one-form Minkowski's inequality and non-conjugate Hölder's inequality are introduced too.

The lecture will be delivered in English