Superior monogamy and polygamy relations and estimates of concurrence

It is well known that any well-defined bipartite entanglement measure $$ obeys $$ th-monogamy relations Eq. (1.1) and assisted measure $$ obeys $$ th-polygamy relations Eq. (1.2). Recently, we presented a class of tighter parameterized monogamy relation for the $$ th $$ power based on Eq. 1.1. This study provides a family of tighter lower (resp. upper) bounds of the monogamy (resp. polygamy) relations in a unified manner. In the first part of the paper, the following three basic problems are focused: (i)tighter monogamy relation for the $$ th ( $$ ) power of any bipartite entanglement measure $$ based on Eq. (1.1);(ii)tighter polygamy relation for the $$ th ( $$ ) power of any bipartite assisted entanglement measure $$ based on Eq. (1.2);(iii)tighter polygamy relation for the $$ th ( $$ ) power of any bipartite assisted entanglement measure $$ based on Eq. (1.2). In the second part, using the tighter polygamy relation for the $$ th ( $$ ) power of CoA, we obtain good estimates or bounds for the $$ th ( $$ ) power of concurrence for any N-qubit pure states $$ under the partition $$ and $$ . Detailed examples are given to illustrate that our findings exhibit greater strength across all the region.