One of the the most often
used results of bifurcation theory is the following theorem. Let C be a compact
mapping from the Banach space X into itself. Suppose that C is such that
C(𝜃) = 𝜃 and the derivative of C exists at x = 𝜃. Then each characteristic
value, μ0, of odd multiplicity of C′(𝜃) is a bifurcation point of C, and to this
bifurcation point there corresponds a continuous branch of eigenvectors of C. The
main result in this paper will show that the above theorem can be extended
to a class of non-compact mapping of the form I − f where f is a k-set
contraction.
