论文标题
$ p $ - 角距离的界限和内部产品空间的特征
Bounds for the $p$-angular distance and characterizations of inner product spaces
论文作者
论文摘要
基于适当改善三角形不平等，我们以$ p $ - 角距离$α_p[x，y] = \ big \ vert \ vert x \ vert x \ vert x \ vert x \ vert x- \ vert y \ vert y \ vert y \ vert y \ vert y \ vert y \ vert^{p-1} y \ big big \ vert in Nord in Nord in Nord in Nord lineal $ x $ x $ x。我们表明，与Dragomir，Hile和Maligranda建立的先前已知的上限相比，我们的估计值更准确。接下来，我们就$ p $ - 角距离进行了几个内部产品空间的特征。特别是，我们证明如果$ | p | \ geq | q | $，$ p \ neq q $，则$ x $是内在的产品空间，并且仅当每个$ x，y \ in x \ setMinus \ in x \ setMinus \ {0 \} $，$ {0 \} $，$ $，$ $ \ frac {{{\ | x \ |^{p}+\ | y \ |^{p}}}}} {\ | x \ |^{q}+\ | y \ | y \ |^{q}}α_q[x [x [x，y]。$ $
Based on a suitable improvement of a triangle inequality, we derive new mutual bounds for $p$-angular distance $α_p[x,y]=\big\Vert \Vert x\Vert^{p-1}x- \Vert y\Vert^{p-1}y\big\Vert$, 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 $x,y\in X\setminus \{0\}$, $${α_p[x,y]}\geq \frac{{\|x\|^{p}+\|y\|^{p} }}{\|x\|^{q}+\|y\|^{q} }α_q[x,y].$$
