Continuation theorems for countably condensing maps (Q2731610)

The authors discuss several classes of essential countably condensing maps and prove fixed point theorems for such classes. However, the authors seem to be unaware of previous work on these topics. Thus, almost all theorems in Section 2 are special cases of results by \textit{M. Väth} [Topol. Methods Nonlinear Anal. 13, No. 2, 341-363 (1999; Zbl 0964.47025) and 16, No. 2, 307-338 (2000; Zbl 0992.47028)]. Moreover, the case of selfmaps of a convex domain with Leray-Schauder condition has been solved by \textit{H. Mönch} [Nonlinear Anal. Theory Methods Appl. 4, 985-999 (1980; Zbl 0462.34041)] and, independently, by \textit{L. Janos} and \textit{M. Martelli} [Univ. Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 16, No. 1, 85-94 (1986; Zbl 0635.47049)]. Although the last cited authors restrict themselves to single-valued maps in Banach spaces, the extension of their technique to multivalued maps in Fréchet spaces is trivial.