Abstract
A unification version of the Perron–Frobenius theorem and the Krein–Rutman theorem for increasing, positively 1-homogeneous, compact mappings is given on ordered Banach spaces without monotonic norm. A Collatz-type minimax characterization of the positive eigenvalue with positive eigenvector is obtained. The power method in computing the largest eigenpair is also extended.
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Chang, K.C. Nonlinear extensions of the Perron–Frobenius theorem and the Krein–Rutman theorem. J. Fixed Point Theory Appl. 15, 433–457 (2014). https://doi.org/10.1007/s11784-014-0191-2
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DOI: https://doi.org/10.1007/s11784-014-0191-2