Hardy–Littlewood–Pólya-type theorems for invex functions

https://doi.org/10.1016/j.camwa.2011.12.039Get rights and content
Under an Elsevier user license
open archive

Abstract

In this paper, the Hardy–Littlewood–Pólya 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.

Keywords

Majorization
Invex function
Pseudo-invex function
Quasi-invex function
Separable vector
Relative invexity

Cited by (0)