On the construction of maximal $p$-cyclically monotone operators

TL;DR

This paper introduces a systematic method for constructing explicit examples of maximal p-cyclically monotone operators, addressing a gap in the literature by providing multiple concrete instances beyond the known case.

Contribution

It presents a novel systematic approach to construct explicit maximal p-cyclically monotone operators, including new examples that extend previous knowledge.

Findings

Provided a systematic construction method for maximal p-cyclically monotone operators.

Generated several explicit examples of such operators.

Extended the known class of maximal 2-cyclically monotone operators.

Abstract

In this paper we deal with the construction of explicit examples of maximal $p$-cyclically monotone operators. To date, there is only one instance of an explicit example of a maximal 2-cyclically monotone operator that is not maximal monotone. We present a systematic way to construct this kind of examples, along with several explicit examples.