Fixed point theorems for maps on cones in Frechet spaces via the projective limit approach

Abstract

We present fixed point results for admissibly compact maps on cones in Fr´echet spaces. We first extend the Krasnosel’ski˘i fixed point theorem with order type cone-compression and cone-expansion conditions. Then, we extend the monotone iterative method to this context. Finally, we present fixed point results under a combination of the assumptions of the previous results. More precisely, we combine a cone-compressing or cone-extending condition only on one side of the boundary of an annulus with an assumption on the existence of an upper fixed point. In addition, we show that the usual monotonicity condition can be weaken