Estimates for the p-angular distance and characterizations of inner product spaces (CROSBI ID 710783)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Krnić, Mario ; Minculete, Nicusor
engleski
Estimates for the p-angular distance and characterizations of inner product spaces
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].
inner product space, normed space, $p$-angular distance, characterization of inner product space, the Hile inequality
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nije evidentirano
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Podaci o prilogu
1-1.
2021.
objavljeno
Podaci o matičnoj publikaciji
Podaci o skupu
International Conference on Analysis and its Applications 2021 (ICAA 2021), Kathmandu University, Dhulikhel, Nepal
predavanje
09.04.2021-11.04.2021
Dhulikhel, Nepal