On calculation of the relative index of a fixed point in the nondegenerate case (Q2491424)

Summary: 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 \(O\) 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.