  In this paper, we select a sample including 141 BEST time-integrated F
spectra and 145 BEST peak flux P spectra observed by the Konus-Wind with known
redshift to recheck the connection between the spectral width and $E_{iso}$ as
well as $L_{iso}$. We define six types of absolute spectral widths. It is found
that all of the rest-frame absolute spectral widths are strongly positive
correlated with $E_{iso}$ as well as $L_{iso}$ for the long burst for both the
F and P spectra. All of the short bursts are the outliers for width-$E_{iso}$
relation and most of the short bursts are consistent with the long bursts for
the width-$L_{iso}$ relation for both F and P spectra. Moreover, all of the
location energy, $E_{2}$ and $E_{1}$, corresponding to various spectral widths
are also positive correlated with $E_{iso}$ as well as $L_{iso}$. We compare
all of the relations with the Amati and Yonetoku relations and find the
width-$E_{iso}$ and width-$L_{iso}$ relations when the widths are at about 90\%
maximum of the $EF_{E}$ spectra almost overlap with Amati relation and Yonetoku
relation, respectively. The correlations of $E_{2}-E_{iso}$, $E_{1}-E_{iso}$
and $E_{2}-L_{iso}$, $E_{1}-L_{iso}$ when the location energies are at 99\%
maximum of the $EF_{E}$ spectra are very close to the Amati and Yonetoku
relations, respectively. Therefore, we confirm the existence of tight
width-$E_{iso}$ and width-$L_{iso}$ relations for long bursts. We further show
that the spectral shape is indeed related to $E_{iso}$ and $L_{iso}$. The Amati
and Yonetoku relations are not necessarily the best relationships to relate the
energy to the $E_{iso}$ and $L_{iso}$. They may be the special cases of the
width-$E_{iso}$ and width-$L_{iso}$ relations or the energy-$E_{iso}$ and
energy-$L_{iso}$ relations.
