Krasnoselskii type fixed point theorems and applications. (English summary) Proc. Amer. Math. Soc. 136 (2008), no. 4, 1213–1220. Summary: “In this paper, we establish two fixed point theorems of Krasnosel ′ skiĭ type for the sum of A + B, where A is a compact operator and the operator I − B may not be injective. Our results extend previous ones. As an application, we apply such results to obtain some existence results for periodic solutions of delay integral equations and then give three instructive examples.