Strongly adequate functions on Banach spaces

TL;DR

This paper explores the concept of strongly adequate functions on Banach spaces, establishing their equivalence with essentially firmly subdifferentiable functions, thereby deepening the understanding of function characterization in functional analysis.

Contribution

It extends the notion of adequate functions, providing a characterization of strongly adequate functions as essentially firmly subdifferentiable on Banach spaces.

Findings

Strongly adequate functions are characterized as essentially firmly subdifferentiable.

The paper reinforces the connection between weakly lower semicontinuous functions and their subdifferentiability properties.

It advances the theoretical framework for analyzing functions on Banach spaces.

Abstract

The notion of adequate function has been recently introduced in order to characterize the essentially strictly functions on a reflexive Banach space among the weakly lower semicontinuous ones. In this paper we reinforce this concept and show that a lower semicontinuous function is essentially firmly subdifferentiable if and only if it is strongly adequate.