LERAY-SCHAUDER, LEFSCHETZ AND KRASNOSELSKII FIXED POINT THEORY IN FRECHET SPACES FOR GENERAL CLASSES OF VOLTERRA OPERATORS

New fixed point theorems for maps (single-valued and multi-valued) between Frechet spaces are presented. The proof relies on fixed point theory in Banach spaces and viewing a Frechet space as the projective limit of a sequence of Banach spaces. In particular we obtain an applicable Leray-Schauder alternative, a Lefschetz fixed point theorem and a Krasnoselskii fixed point theorem in Frechet spaces for general classes of maps.