On Rational Recursive Sequences

We study the global asymptotic behavior, the oscillatory character, and the periodic nature of all positive solutions of the recursive sequences xn + 1 = (a + ∑k − 1i = 0bixn − i)/xn − kn = 0, 1, 2, ..., and xn + 1 = (a + bxn)/(A + xn − k), n = 0, 1, 2, ..., where a, b, b0, ..., bk − 1 and A are nonnegative numbers and k is a positive integer.