Convexity properties of functions defined on metric Abelian groups

TL;DR

This paper introduces and explores convexity-related properties for functions on metric Abelian groups, extending classical convexity concepts and characterizations to this broader mathematical setting.

Contribution

It defines quasiconvexity, Wright convexity, and convexity on metric Abelian groups and establishes their properties and characterizations, extending known results to this new context.

Findings

Characterization of convexity properties on metric Abelian groups

Structural properties of convex function classes in this setting

Extension of classical convexity results

Abstract

The notions of quasiconvexity, Wright convexity and convexity for functions defined on a metric Abelian group are introduced. Various characterizations of such functions, the structural properties of the functions classes so obtained are established and several well-known results are extended to this new setting.