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

Autori
Krnić, Mario ; Minculete, Nicusor

Izvornik
Mediterranean journal of mathematics (1660-5446) 18 (2021), 4; 140, 22

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

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

Sažetak
Based on a suitable improvement of a triangle inequality, 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