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A. V. Guminskaya, P. P. Zabreiko, "On calculation of the relative index of a fixed point in the nondegenerate case", Abstract and Applied Analysis, vol. 2006, Article ID 086173, 11 pages, 2006. https://doi.org/10.1155/AAA/2006/86173
On calculation of the relative index of a fixed point in the nondegenerate case
The paper is devoted to the calculation of the index of a zero and the asymptotic index of a linear completely continuous nonnegative operator. Also the case of a nonlinear completely continuous operator whose domain and image are situated in a closed convex set of a Banach space is considered. For this case, we formulate the rules for calculating the index of an arbitrary fixed point and the asymptotic index under the assumption that the corresponding linearizations exist and the operators of derivative do not have eigenvectors with eigenvalue in some wedges.
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Copyright © 2006 A. V. Guminskaya and P. P. Zabreiko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.