More on reverse triangle inequality in inner product spaces

Refining some results of S. S. Dragomir, several new reverses of thegeneralized triangle inequality in inner product spaces are given. Amongseveral results, we establish some reverses for the Schwarz inequality. Inparticular, it is proved that if $a$ is a unit vector in a real or complexinner product space $(H;< .,.>)$, $r, s>0, p\in(0,s], D=\{x\in H,\|rx-sa\|\leqp\}, x_1, x_2\in D-\{0\}$ and $\alpha_{r,s}=\min\{\frac{r^2\|x_k\|^2-p^2+s^2}{2rs\|x_k\|}: 1\leq k\leq 2 \}$,then $$\frac{\|x_1\|\|x_2\|-Re< x_1,x_2>}{(\|x_1\|+\|x_2\|)^2}\leq\alpha_{r,s}.$$Comment: 12 page