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In this paper, the concept of eigenvalue is introduced to the monotone homogeneous mapping pairs (f,g), and its existence and uniqueness are established successfully under the boundedness of some orbits of f,g in the Hilbert semi-norm. Also, the Collatz–Wielandt min–max type property is obtained for such a class of mapping pairs. In particular, the nonlinear Perron–Frobenius property for nonnegative...
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