On the Jensen convexity of quasideviation and Bajraktarevi\'c means

TL;DR

This paper characterizes the Jensen convexity of quasideviation and Bajraktarević means without extra regularity assumptions, extending previous work on quasiarithmetic means.

Contribution

It provides a new, more general characterization of Jensen convexity for these means, removing unnecessary regularity constraints.

Findings

Characterization of Jensen convexity for quasideviation means

Characterization of Jensen convexity for Bajraktarević means

Extension of previous results on quasiarithmetic means

Abstract

Motivated by the characterization theorem about the Jensen convexity of quasiarithmetic means obtained by the authors in 2021, our main goal is to establish a characterization of the Jensen convexity of quasideviation as well as of Bajraktarevi\'c means without any additional and unnatural regularity assumptions.