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The Lefschetz Fixed Point Theorem
The Lefschetz Fixed Point Theorem generalizes a collection of fixed point theorems for different topological spaces, including maps on the n-sphere and the n-disk. Although the theorem is easily written in terms of compact manifolds, in this paper we will work entirely with topological spaces that are simplicial complexes or retracts of simplicial complexes. After developing the fundamentals of...
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The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of ...
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A Lefschetz-type coincidence theorem for two maps f, g : X → Y from an arbitrary topological space to a manifold is given: Ifg = λfg, that is, the coincidence index is equal to the Lefschetz number. It follows that if λfg 6= 0 then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y ...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1975
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-88-2-103-115