Abstract
We study mapsTfor whichJ−Tis pseudo-monotone; we call suchTa PM-map. This includes compact maps in suitable spaces and pseudo-contractive maps in Hilbert spaces. We study variational inequalities in a situation which was previously done only whenTis compact. We show that our variational inequalities are well suited to treating existence of fixed points for generalized inward (in particular, weakly inward) PM-maps in Hilbert spaces. Our new results on existence of fixed points generalizes many earlier results obtained by using other methods. An application to homogeneous integral equations is provided.
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