In the paper, three basic properties of the logarithmically N-alternating
monotonic functions are established and the monotonicity results
of some functions involving the gamma and q-gamma functions, which are obtained
in [W. E. Clark and M. E. H. Ismail, Inequalities involving gamma and
psi functions, Anal. Appl. (Singap.) 1 (2003), no. 1, 129–140.], are generalized
to the logarithmically N-alternating monotonicity.