Gauge integrals and selections of weakly compact valued multifunctions
  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. 
D. Candeloro, L. Di Piazza, K. Musial, A.R. Sambucini
math.FA