An extension of Guoʹs theorem via k-image-contractive retractions Original Research Article

Let X be a infinite-dimensional Banach space. We generalize Guoʹs Theorem [D.J. Guo, Eigenvalues and eigenvectors of nonlinear operators, Chinese Ann. Math. 2 (1981) 65–80 [English]] to k-ψψ-contractions and condensing mappings, under a condition which depends on the infimum kψkψ of all k⩾1k⩾1 for which there exists a k-ψψ-contractive retraction of the closed unit ball of the space X onto its boundary.