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Abstract and Applied Analysis
Volume 2006 (2006), Article ID 86173, 11 pages
http://dx.doi.org/10.1155/AAA/2006/86173

On calculation of the relative index of a fixed point in the nondegenerate case

Mechanics and Mathematics Faculty, Belarusian State University, Independence Avenue 4, Minsk 220050, Belarus

Received 26 June 2005; Accepted 1 July 2005

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.

Abstract

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 A whose domain and image are situated in a closed convex set Q 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 1 in some wedges.