Naslov
Estimates for the p-angular distance and characterizations of inner product spaces

Autori
Krnić, Mario ; Minculete, Nicusor

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
International Conference on Analysis and its Applications 2021 (ICAA 2021), Kathmandu University, Dhulikhel, Nepal

Mjesto i datum
Dhulikhel, Nepal, 09.04.2021. - 11.04.2021

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
inner product space, normed space, $p$-angular distance, characterization of inner product space, the Hile inequality

Sažetak
In this talk we derive new mutual bounds for $p$-angular distance $\alpha_p[x, y]=\big\Vert \Vert x\Vert^{; ; ; p-1}; ; ; x- \Vert y\Vert^{; ; ; p-1}; ; ; y\big\Vert$, in a normed linear space $X$. We show that our estimates are more accurate than the previously known upper bounds established by Dragomir, Hile and Maligranda. Next, we give several characterizations of inner product spaces with regard to the $p$-angular distance. In particular, we prove that if $|p|\geq |q|$, $p\neq q$, then $X$ is an inner product space if and only if for every $x, y\in X\setminus \{; ; ; 0\}; ; ; $, $${; ; ; \alpha_p[x, y]}; ; ; \geq \frac{; ; ; {; ; ; \|x\|^{; ; ; p}; ; ; +\|y\|^{; ; ; p}; ; ; }; ; ; }; ; ; {; ; ; \|x\|^{; ; ; q}; ; ; +\|y\|^{; ; ; q}; ; ; }; ; ; \alpha_q[x, y].

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA