Fixed Point Theory for Self Maps between Fr´echet Spaces

Using Krasnoselskii’s fixed point theorem in a cone, we present a new fixed point theory for multivalued self maps between Fr´echet spaces. Our analysis relies on a diagonal process and a result on hemicompact maps due to K. K. Tan and X. Z. Yuan Ž1994, J. Math. Anal. Appl. 185, 378 390.. An application is given to illustrate the theory.