ABSTRACT
In Chapter III we first present constructive fixed-point and surjectivity theorems for generalized projectionally compact (Pγ compact) mappings whose study was initiated by the author in [202,206] and studied further by the writer (see [203,213,221]) and other authors (see [46,51,52,60,61,64,70,125,201,236,307]). For historical reasons let me add that the first such theorems for P0-compact mappings were obtained by the author in [202], where it was shown that in addition to classical and other fixed-point theorems, the theorem included the surjectivity results of Minty, Browder, and Shinbrot for maps λI – F with F monotone decreasing and either continuous, demicontinuous, or weakly continuous. This fact provided the main initial motivation for the study of Pγ-compact and later of A-proper mappings.
