Naslov
Chaotic order among means of positive operators

Autori
Pečarić, Josip ; Mićić, Jadranka

Izvornik
Scientiae mathematicae Japonicae (1346-0862) 57 (2003), 1; 139-148

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

Ključne riječi
operator order; chaotic order; power mean

Sažetak
The aim of this paper is to generalize the above mentioned as follows: \\ \noindent Let $M_{; ; k}; ; ^{; ; [r]}; ; ({; ; \mathbf{; ; A}; ; }; ; ; w) := (\sum_{; ; j=1}; ; ^{; ; k}; ; \omega_j \ A_j^{; ; r}; ; )^{; ; 1/r}; ; $ ($r \in {; ; \mathbf{; ; R}; ; }; ; \backslash \{; ; 0 \}; ; $) be weighted power mean of posi\-ti\-ve operators $A_j$, ${; ; \mathsf{; ; Sp}; ; }; ; (A_j) \subseteq [m, M]$ ($j=1, \ldots, k$), $0<m<M$ and $\omega_j \in {; ; \mathbf{; ; R}; ; }; ; _+$, $\sum_{; ; j=1}; ; ^k \omega_j =1$. Let $M_{; ; k}; ; ^{; ; [0]}; ; ({; ; \mathbf{; ; A}; ; }; ; ; w)$ be the corresponding chaotic geometric mean. If $r \leq s$ then realconstants $\alpha_1$ and $\alpha_1$ such that \(\alpha_2 M_{; ; k}; ; ^{; ; [s]}; ; ({; ; \mathbf{; ; A}; ; }; ; ; w) \leq M_{; ; k}; ; ^{; ; [r]}; ; ({; ; \mathbf{; ; A}; ; }; ; ; w) \leq \alpha_1 M_{; ; k}; ; ^{; ; [s]}; ; ({; ; \mathbf{; ; A}; ; }; ; ; w), \) are determined, when $r \not \in \langle -1, 1 \rangle$, $r \neq 0$ or $s \not \in \langle -1, 1 \rangle$, $s \neq 0$. Furthermore, if $r \leq s$ then real constant $\Delta$ such that \( \Delta M_{; ; k}; ; ^{; ; [s]}; ; ({; ; \mathbf{; ; A}; ; }; ; ; w) \ll M_{; ; k}; ; ^{; ; [r]}; ; ({; ; \mathbf{; ; A}; ; }; ; ; w) \ll M_{; ; k}; ; ^{; ; [s]}; ; ({; ; \mathbf{; ; A}; ; }; ; ; w), \) is determined.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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