On maximal elements with applications to abstract economies, fixed point theory and eigenvector problems

Two existence theorems of maximal elements in H-spaces are obtained without compactness. More accurately, we deal with the correspondence to be of L-majorized mappings in the setting of noncompact strategy sets but merely requiring a milder coercive condition. As applications, we obtain an equilibrium existence theorem for general abstract economies, a new fixed point theorem, and give a sufficient condition for the existence of solutions of the eigenvector problem (EIVP).