A class of k-log-convex functions and their applications to some special functions.

Let a and b be two real numbers and f be a positive and differentiable function on an interval I. The authors establish the i-log-convex or i-log-concave properties for i∈ of the function [f(bx)]a/[f(ax)]b for ax∈I and bx∈I when the function uk-1[ln f(u)](k) for k∈ is monotonic and apply these properties to deduce some known and new conclusions related to some special functions, such as the gamma function, Riemann's zeta function, complete elliptic integrals, exponential mean, and extended mean values. [ABSTRACT FROM AUTHOR]