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Perron-Frobenius problem for weakly sublinear maps in a euclidean positive orthant

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Abstract

We will generalize the Perron-Frobenius theorem for square matrices to nonlinear maps, adding the condition of subadditivity (called (C3)) in the sequel to the usual conditions. In the terminology of economics, we are concerned with the nonlinear Leontief model. One of the main results is the canonical decomposition theorem. To accomplish this result, it is also necessary to modify slightly the definition of indecomposability in the earlier works.

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Authors and Affiliations

  1. Faculty of Engineering, Doshisha University, 602, Kyoto, Japan

    Yorimasa Oshime

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  1. Yorimasa Oshime
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Oshime, Y. Perron-Frobenius problem for weakly sublinear maps in a euclidean positive orthant. Japan J. Indust. Appl. Math. 9, 313 (1992). https://doi.org/10.1007/BF03167569

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  • DOI: https://doi.org/10.1007/BF03167569

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