Cone Monotonicity: Structure Theorem, Properties, and Comparisons to Other Notions of Monotonicity

TL;DR

This paper introduces new definitions of cone monotonicity in two dimensions, explores their properties, compares them to existing notions, and discusses their theoretical significance.

Contribution

It proposes two novel definitions of cone monotonicity, analyzes their properties, and clarifies their relationship with existing concepts in the literature.

Findings

Introduced two new definitions of cone monotonicity

Established relationships between new and existing notions

Provided examples illustrating the concepts

Abstract

In search of a meaningful 2-dimensional analog to mono- tonicity, we introduce two new definitions and give examples of and dis- cuss the relationship between these definitions and others that we found in the literature. Note: After we published the article in Abstract and Applied Analysis and after we searched multiple times for previous work, we discovered that Clarke at al. had introduced the definition of cone monotonicity and given a characterization. See the addendum at the end of this paper for full reference information.