Gauge integrals and selections of 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.

arXiv comment21 pages

References in corpus (5)

• An extension of the Birkhoff integrability for multifunctions
• Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures
• A note on comparison between Birkhoff and McShane-type integrals for multifunctions
• Comparison between some norm and order gauge integrals in Banach lattices
• Set valued integrability in non separable Fréchet spaces and applications

Cited by in corpus (11)

• Relations among Gauge and Pettis integrals for $cwk(X)$-valued multifunctions
• Some new results on integration for multifunction
• Properties of the Riemann-Lebesgue integrability in the non-additive case
• Convergence for varying measures
• Atomicity related to non-additive integrability
• Kuelbs-Steadman spaces for Banach space-valued measures
• Multifunctions determined by integrable functions
• Convergence for varying measures in the topological case
• A Girsanov Result through Birkhoff Integral
• A survey on composition operators on some function spaces
• A Girsanov result for the Pettis integral