Naslov
Characterizations of $\delta$--order associated with Kantorovich type operator inequalities

Autori
Mićić, Jadranka ; Pečarić, Josip

Izvornik
Scientiae mathematicae Japonicae (1346-0862) 18 (2005); 597-603

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

Ključne riječi
Operator order; chaotic order; Kantorovich inequality; grand Furuta inequality

Sažetak
In this note, we obtain more precise estimations than the constants are given in the paper by M.Fujii, E.Kamei and Y.Seo, {; ; \it Kantorovich type operator inequalities via grand Furuta inequality}; ; , Sci. Math., {; ; \bf 3}; ; (2000), 263--272. Among other, we show that the following statements are mutually equivalent for each $\delta \in (0, 1]$: (i) $ K(m^{; ; \frac{; ; (p-\delta)s}; ; {; ; n}; ; }; ; , M^{; ; \frac{; ; (p-\delta)s}; ; {; ; n}; ; }; ; , n+1)^{; ; \frac{; ; 1}; ; {; ; s}; ; }; ; A^{; ; p}; ; \geq B^{; ; p}; ; $ for any $n>0$, $s \geq 1$, $p \geq \delta$ with $ (p-\delta )s \geq n \delta $. (ii) $K(m^{; ; \delta}; ; , M^{; ; \delta}; ; , \frac{; ; p}; ; {; ; \delta}; ; ) A^{; ; p}; ; \geq B^{; ; p}; ; \qquad \mbox{; ; for any $p \geq \delta$ }; ; $. For each $\delta \in (0, 1]$ $$K(m^{; ; \frac{; ; (p-\delta)s}; ; {; ; n}; ; }; ; , M^{; ; \frac{; ; (p-\delta)s}; ; {; ; n}; ; }; ; , n+1)^{; ; \frac{; ; 1}; ; {; ; s}; ; }; ; \geq K(m^{; ; \delta}; ; , M^{; ; \delta}; ; , \frac{; ; p}; ; {; ; \delta}; ; )$$ holds for any $n>0$, $s \geq 1$, $p \geq \delta$ such that $ (p-\delta )s \geq n \delta $.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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