Fixed Points of h-completely Continuous Multivalued Mappings and Inequalities in Spaces with the Cone

Abstract

In the first part of the paper a new class of multivalued mappings is introduced and studied. This mappings have convex but non-compact images. For the mappings of this particular class we are proving fixed points theorems, which are used in the second part of the paper to study solvability of inequalities in spaces with the cone.