Fixed-point properties of the Mordukhovich differential operator

TL;DR

This paper explores fixed-point properties of the Mordukhovich differential operator in Banach spaces, focusing on metric projection operators onto various convex and closed sets, revealing new insights into their behavior.

Contribution

It provides new results on the fixed-point properties of the Mordukhovich differential operator for specific set-valued and single-valued mappings in Banach spaces.

Findings

Fixed-point properties for metric projections onto closed convex sets

Analysis of the operator on positive cones in l2 and l1

Results for polynomial sets in C[0,1]

Abstract

In this paper, we investigate some fixed-point properties of the Mordukhovich differential operator of set valued mappings (or, single valued mappings) on Banach spaces. In particular, we study the fixed-point properties of the Mordukhovich differential operator for the metric projection operator onto some closed and convex subsets in Banach spaces, such as, closed balls in Banach spaces, positive cones in real spaces l2 and l1 and sets of polynomials in C[0, 1].