Mordukhovich derivatives of the normalized duality mapping in Banach spaces

TL;DR

This paper studies the Mordukhovich derivatives of the normalized duality mapping in various Banach spaces, providing insights into their properties in uniformly convex, smooth, and other classical spaces.

Contribution

It offers new analysis of Mordukhovich derivatives for the duality mapping across different Banach space classes, extending existing theoretical understanding.

Findings

Derived properties of Mordukhovich derivatives in uniformly convex and smooth spaces

Extended analysis to classical spaces L1 and C[0,1]

Enhanced understanding of duality mappings in Banach space theory

Abstract

In this paper, we investigate some properties of the Mordukhovich derivatives of the normalized duality mapping in Banach spaces. For the underlying spaces, we consider three cases: uniformly convex and uniformly smooth Banach space lp; general Banach spaces L1 and C[0,1].