engleski

On logarithmic convexity for Giaccardi-s difference

In this paper, the Giaccardi’s difference is considered in some special cases. By utilizing two classes of the convex functions, the logarithmic convexity of the Giaccardi’s difference is proved. The positive semi-definiteness of the matrix generated by Giaccardi’s difference is shown. Related means of Cauchy type are defined and monotonicity property of these means is proved. The related mean value theorems of Cauchy type are also given.

Convex function; log-convex function; Giaccardi’s inequality; mean value theorems

nije evidentirano