Hardy-Littlewood-Polya-type theorems for invex functions
In this paper, the Hardy-Littlewood-Polya theorem on majorization is extended from convex functions to invex ones. Some variants for pseudo-invex and quasi-invex functions are also considered. The framework used is that of similarly separable vectors. The results obtained are illustrated for monotonic, monotonic in mean, and star-shaped vectors, respectively. Applications to relative invexity are given. (C) 2011 Elsevier Ltd. All rights reserved.
invex function majorization quasi-invex function separable vector relative invexity pseudo-invex function