Let X be a infinite-dimensional Banach space. We generalize Guo''s Theorem [D.J. Guo, Eigenvalues and eigenvectors of nonlinear operators, Chinese Ann. Math. 2 (1981) 65–80 [English]] to k-ψ-contractions and condensing mappings, under a condition which depends on the infimum kψ of all k \ge1 for which there exists a k-ψ-contractive retraction of the closed unit ball of the space X onto its boundary.
CAPONETTI, D., TROMBETTA, A., TROMBETTA, G. (2006). An extension of Guo's theorem via k-psi-contractive retraction. NONLINEAR ANALYSIS, 64 (9), 1897-1907.
An extension of Guo's theorem via k-psi-contractive retraction
CAPONETTI, Diana;
2006-01-01
Abstract
Let X be a infinite-dimensional Banach space. We generalize Guo''s Theorem [D.J. Guo, Eigenvalues and eigenvectors of nonlinear operators, Chinese Ann. Math. 2 (1981) 65–80 [English]] to k-ψ-contractions and condensing mappings, under a condition which depends on the infimum kψ of all k \ge1 for which there exists a k-ψ-contractive retraction of the closed unit ball of the space X onto its boundary.
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