Convergence of certain bounded sequences Original Research Article

Let V be a nontrivial finite-dimensional real vector space, ordered by a cone K, and equipped with the standard norm topology. If K contains no affine line, then for each α1, …, αp ε image the following statements are equivalent: (i) Every bounded sequence (xn)∞n = 1 in V satisfying image is convergent; (ii) The polynomial P(t) = tp − α1tp−1 − … − αp−1t − αp has 1 as a zero and has no other complex zeroes of absolute value 1. If αj greater-or-equal, slanted 0 for J = 1, ….p, then (ii) can be replaced by (ii)* σpj=1 αj = 1, and the natural numbers j less-than-or-equals, slant p satisfying αj > 0 are relatively prime.