Abstract.
In Sections 2 and 3 of this paper we refine and generalize theorems of Nussbaum (see [42]) concerning the approximate fixed point index and the fixed point index class. In Section 4 we indicate how these results imply a wide variety of asymptotic fixed point theorems. In Section 5 we prove a generalization of the mod p theorem: if p is a prime number, f belongs to the fixed point index class and f satisfies certain natural hypothesis, then the fixed point index of f p is congruent mod p to the fixed point index of f. In Section 6 we give a counterexample to part of an asymptotic fixed point theorem of A. Tromba [55]. Sections 2, 3, and 4 comprise both new and expository material. Sections 5 and 6 comprise new results.
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This paper is dedicated to Felix Browder on the occasion of his eightieth birthday and in recognition of his many contributions to nonlinear analysis
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Mallet-Paret, J., Nussbaum, R.D. Asymptotic fixed point theory and the beer barrel theorem. J. fixed point theory appl. 4, 203–245 (2008). https://doi.org/10.1007/s11784-008-0095-0
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DOI: https://doi.org/10.1007/s11784-008-0095-0