Global Generalizations of the Birkhoff-Kellogg Theorem on Set-Contraction Operators

The purpose of this paper is to give some global generalizations of the Birkhoff—Kellogg theorem on set-contraction operators.In this paper,we 8uppose that X is an infinite-dimensional Banach space and A:x→X is a κ-set-contraction operator,0≤κ< ∞.we shall denote by E the Banach space R~1×X with norm ‖(λ,χ)‖=(λ~2 ‖χ‖~2)~1/2.The c1losure of the set of nonZero solutions of the equation χ=λAχ will be denoted by L,i.e.,