Application and issues in abstract convexity

TL;DR

This paper explores the application of abstract convexity to function approximation and examines its connection with axiomatic convexity, highlighting theoretical aspects and potential for future practical use.

Contribution

It introduces the application of abstract convexity to function approximation and investigates its relationship with axiomatic convexity, expanding theoretical understanding.

Findings

Abstract convexity offers a framework for function approximation.

Connections with axiomatic convexity are established.

The area has potential for practical applications in the future.

Abstract

The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this area has not found many practical applications yet. In this paper we study the application of abstract convexity to function approximation. Another important research direction addressed in this paper is the connection with the so-called axiomatic convexity.