General monotonicity

TL;DR

This paper uses convex analysis to characterize maximal n-monotonicity, extending the well-known theory of monotonicity with new mathematical insights and illustrative examples.

Contribution

It provides novel characterizations of maximal n-monotonicity using convex analysis, broadening the theoretical understanding of this mathematical concept.

Findings

New convex analysis-based characterizations of maximal n-monotonicity

Illustrative examples demonstrating the characterizations

Extension of classical monotonicity theory to n-monotonicity

Abstract

This article employs techniques from convex analysis to present characterizations of (maximal) $n-$monotonicity, similar to the well-established characterizations of (maximal) monotonicity found in the existing literature. These characterizations are further illustrated through examples.