Existence of Fixed Points of Noncompact Mappings: Sophisticated Forms of Iteration Scheme for Noncompact Mappings

Abstract

The results presented for various classes of nonlinearmappings (contractive, strictly pseudo contractive, pseudo contractive) may beconsidered as somewhat sophisticated, sharpened forms of the classicaliteration scheme (the method of successive approximations) ofPicard-Banach-Cacciopoli et al. that work in contexts in which the classicaliteration scheme no longer applies (and in particular, outside the class ofstrictly contractive mappings). We have restricted the discussion to the caseof mappings defined in Hilbert space both to avoid technical complications inthe presentation of the results and proofs.