An improvement on a new upper bound for moduli of eigenvalues of iterative matrices

In this paper, some improvements on [Int. J. Comput. Math. 80 (June) (2003) 799–803] are presented for a bound for moduli of eigenvalues of iterative matrices. And subsequently, we investigate the relationships among them and show that the new bounds are better than the earlier ones [Int. J. Comput. Math. 53 (1994) 203–217; J. Comput. Math. 7 (2) (1986) 41–46; Int. J. Comput. Math. 80 (June) (2003) 799–803] under some conditions.