Bounds for the 1-norm of the inverses of some triangular matrices

In this paper, we find bounds for the 1-norm of the inverses of triangular matrices whose columns may decrease to zero. These results complement those obtained by Berenhaut et al. in [1] where the columns cannot decrease to zero. Also, we extend the 1-norm estimates obtained for Toeplitz matrices, by Liu et al. in [5], to a non-Toeplitz class. Finally, we construct a class of matrices where the estimates obtained are the best.