engleski

3-convex functions and generalizations of an inequality of Hardy-Littlewood-Polya

In this paper, we present some generalizations of an inequality of Hardy-Littlewood-Polya. We give the n-exponential convexity and log-convexity of the functions associated with the linear functionals defined as the non-negative differences of the generalized inequalities and prove the monotonicity property of the generalized Cauchy means obtained via these functionals. Finally, we give several examples of the families of functions for which the results can be applied.

non-increasing sequence in weighted mean; convex function; 3-convex function; n-exponential and logarithmic convexity; mean value theorems; divided difference

nije evidentirano