Naslov
The Beckenbach-Dresher inequality in the $\Psi$- direct sums of spaces and related results

Autori
Nikolova, Ludmila ; Persson, Lars-Erik ; Varošanec, Sanja

Izvornik
Journal of inequalities and applications (1029-242X) (2012), 7; 1-14

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
inequalities; the Beckenbach-Dresher inequality; concave function; inverse Minkowski's inequality; $\psi$-direct sum; the Lorentz sequence space

Sažetak
Let $\tilde{; ; ; \psi}; ; ; :[0, 1] \rightarrow {; ; ; \bf R}; ; ; $ be a concave function with $\tilde{; ; ; \psi}; ; ; (0)=\tilde{; ; ; \psi}; ; ; (1)=1$. There is a corresponding map $\|.\|_{; ; ; \tilde{; ; ; \psi}; ; ; }; ; ; $ for which the inverse Minkowski inequality holds. Several properties of that map are obtained. Also, we consider the Beckenbach-Dresher type inequality connected with $\psi$-direct sums of Banach spaces and of ordered spaces. In the last section we investigate the properties of functions $\psi_{; ; ; \omega, q}; ; ; $ and $\| . \|_{; ; ; \omega, q}; ; ; $, ($0<\omega <1, q<1$) related to the Lorentz sequence space. Other posibilities for parameters $\omega$ and $q$ are considered, the inverse H\" older inequalities and more variants of the Beckenbach-Dresher inequalities are obtained.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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