Generalized Leray-Schauder principles for compact admissible multifunctions (Q1909711)

The author introduces the interesting class of admissible multifunctions. With the assumption that these multifunctions assume values contained in some compact subset of the codomain, the author proves fixed point theorems in locally convex topological vector spaces for these maps satisfying the famous Leray-Schauder boundary condition. The results are established without using the degree theory and extend well-known results, e.g. that one of \textit{L. Gorniewicz}, \textit{A. Granas} and \textit{W. Kryszewski} [C. R. Acad. Sci., Paris, Sér I 307, 489-492 (1988; Zbl 0665.54030)].