Gauge integrals and selections of weakly compact valued multifunctions

TL;DR

This paper investigates various gauge integrals for multifunctions with values in convex, weakly compact subsets of Banach spaces, focusing on the existence of integrable selections in the same sense.

Contribution

It introduces new results on the existence of integrable selections for gauge integrals of weakly compact valued multifunctions in Banach spaces.

Findings

Existence of integrable selections for gauge integrals established.

Comparison of different gauge integrals for multifunctions.

Applications to convex and weakly compact valued multifunctions.

Abstract

In the paper Henstock, McShane, Birkhoff and variationally multivalued integrals are studied for multifunctions taking values in the hyperspace of convex and weakly compact subsets of a general Banach space X. In particular the existence of selections integrable in the same sense of the corresponding multifunctions has been considered.