Fixed Point Principles for Cones of a Banach Space for the Multivalued Maps Differentiable at the Origin and Infinity

Abstract

AbstractIn [6] and [7], Krasnosel'skiĭ proved several fundamental fixed point principles for operators leaving invariant a cone in a Banach space. In [9], Nussbaum extended one of the results, the theorem about compression and expansion of a cone, to k-setcontraction maps, k < 1. Other versions for completely continuous maps were given by Fournier-Peitgen [2] and G. Fournier [1].The purpose of this paper is to generalise some of these results to upper semi continuous multivalued maps which are K-set contractions, k < 1, and differentiable at the origin and infinity.