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- W4313165393 abstract "Let $ C $ be a closed cone with nonempty interior $ {{C}}^circ $ in a Banach space. Let $ f:{{C}}^circ rightarrow {{C}}^circ $ be an order-preserving subhomogeneous function with a fixed point in $ {{C}}^circ $. We introduce a condition which guarantees that the iterates $ f^k(x) $ converge to a fixed point for all $ x in {{C}}^circ $. This condition generalizes the notion of type K order-preserving for maps on $ mathbb{R}^n_{>0} $. We also prove that when iterates converge to a fixed point, the rate of convergence is always R-linear in two special cases: for piecewise affine maps and also for order-preserving, homogeneous, analytic, multiplicatively convex functions on $ mathbb{R}^n_{>0} $. This later category includes the maps associated with the homogeneous eigenvalue problem for nonnegative tensors." @default.
- W4313165393 created "2023-01-06" @default.
- W4313165393 creator A5021081744 @default.
- W4313165393 date "2023-01-01" @default.
- W4313165393 modified "2023-09-26" @default.
- W4313165393 title "Convergence of iterates in nonlinear Perron-Frobenius theory" @default.
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- W4313165393 doi "https://doi.org/10.3934/dcdsb.2022244" @default.
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