A class of expansive-type Krasnosel’skii fixed point theorems

In this paper, we establish some new fixed point theorems for the sum of two operators. In particular, one new theorem complements the well-known Krasnosel’skii fixed-point theorem in the sense that the mapping TT is expansive rather than contractive. Some previous and related results are extended and developed. As an application to one of our main results, the existence of periodic solutions for some nonlinear integral equation is considered.