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Fixed point theorems based on Leray-Schauder degree

Svatopluk Fučík

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Abstract

Introductlon.Thla notě deals with the existence of the aolutlon of the equation Fz » z • The teohnique ušed here la the eo-called Leray-Sohauder topological degree # Thia method haa been largely ušed by Altman [1], J. Cronin 12], Leray and Sehauder [6] and othera* In thla páper thera ia given m generallzation of Altman's reault [1] (eee Remark 2)« The ořem 8 ia the extending of The ořem 7 for a speciál oase.Other theorema are well known, but the proafa are baaed on topological degree theory (see Theorem 1 and Theořem 10)•

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Introductlon.Thla notě deals with the existence of the aolutlon of the equation Fz » z • The teohnique ušed here la the eo-called Leray-Sohauder topological degree # Thia method haa been largely ušed by Altman [1], J. Cronin 12], Leray and Sehauder [6] and othera* In thla páper thera ia given m generallzation of Altman's reault [1] (eee Remark 2)« The ořem 8 ia the extending of The ořem 7 for a speciál oase.Other theorema are well known, but the proafa are baaed on topological degree theory (see Theorem 1 and Theořem 10)•

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Available abstract

Introductlon.Thla notě deals with the existence of the aolutlon of the equation Fz » z • The teohnique ušed here la the eo-called Leray-Sohauder topological degree # Thia method haa been largely ušed by Altman [1], J. Cronin 12], Leray and Sehauder [6] and othera* In thla páper thera ia given m generallzation of Altman's reault [1] (eee Remark 2)« The ořem 8 ia the extending of The ořem 7 for a speciál oase.Other theorema are well known, but the proafa are baaed on topological degree theory (see Theorem 1 and Theořem 10)•

Key concepts: Degree (music), Mathematics, Schauder fixed point theorem, Fixed-point theorem, Point (geometry), Discrete mathematics, Combinatorics, Brouwer fixed-point theorem

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