An intersection theorem in \(L\)-convex spaces with applications (Q2573453)

Let \([x,y]\) be an order interval in an ordered Banach space and \(A,B:[x,y]\mapsto P_{cl} X\) be two multivalued mappings. Under some compactness conditions, it is proved that the operator inclusion \( x\in Ax+Bx\) has a solution in \([x,y]\). In the last section, this result is used to prove the existence of solutions for an integral inclusion.