Bounds on the inverse of nonnegative triangular matrices with monotonicity properties

Some bounds on the entries and on the norm of the inverse of triangular matrices with nonnegative and monotone entries are found. All the results are obtained by exploiting the properties of the fundamental matrix of the recurrence relation which generates the sequence of the entries of the inverse matrix. One of the results generalizes a theorem contained in a recent article of one of the authors about Toeplitz matrices.