Quasidense monotone multifunctions

TL;DR

This paper explores quasidense monotone multifunctions in Banach spaces, providing characterizations, examining Fitzpatrick extensions, and linking quasidensity to maximality and type (FPV) and (FP).

Contribution

It offers new characterizations of quasidense multifunctions and establishes their relation to maximality and Fitzpatrick extensions in Banach spaces.

Findings

Quasidense multifunctions are characterized via sum theorems.

Quasidensity implies type (FPV) and strong maximality for closed monotone multifunctions.

Quasidensity is equivalent to type (FP).

Abstract

In this paper, we discuss quasidense multifunctions from a Banach space into its dual, and use the two sum theorems proved in a previous paper to give various characterizations of quasidensity. We investigate the Fitzpatrick extension of such a multifunction. We prove that, for closed monotone multifunctions, quasidensity implies type (FPV) and strong maximality, and that quasidensity is equivalent to type (FP). This version differs from Version 3 in that a few minor errors have been corrected.