Positive eigenvalues of countably contractive maps
With the aid of degree theory for admissible maps due to Vath [1], we prove that a countably contractive self-map defined on a normal cone in a real Banach space has a positive eigen-value under certain condition. This includes a result of Massabo and Stuart [2] for set contractions. (C) 2003 Elsevier Ltd. All rights reserved.
eigenvalues countably contractive maps measures of noncompactness