RELATIVE STABILITY FOR ASCENDING AND POSITIVELY HOMOGENEOUS OPERATORS ON BANACH-SPACES

For a closed convex cone K in a real Banach space with a norm increasing on K, and a selfmapping T of K which is continuous, positively homogeneous, and ascending it is shown that the nonlinear eigenvalue problem Tx* = lambda*x* has a unique solution x* is an element of K - {0} (up to a scalar), lambda* is an element of R(+) which is relatively stable in the sense that for a suitable function c of K into R(+) [GRAPHICS] Moreover, an estimate for the speed of convergence is given. (C) 1994 Academic Press, Inc.