An Extension and Refinement of the Brouwer-Schauder-Tychonoff Fixed Point Theorem [PDF]
In this paper, we present the Brouwer-Schauder-Tychonoff fixed point theorem on locally convex spaces as the following extension and improvement: Suppose that S is a compact star-shaped subset with respect to p in S with its convexity index alpha(p)>0. Then every continuous self-mapping f has one of the following two properties: (a) The point p is
Lixin Cheng, Chulei Liu, Wen Zhang
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A Tropical Version of the Schauder Fixed Point Theorem [PDF]
, 2009 A tropical version of the Schauder fixed point theorem for compact subsets of tropical linear spaces is proved.
G. B. Shpiz, G. L. Litvinov
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Applications of Schauder's Fixed-point theorem with respect to iterated functional equations
Applied Mathematics Letters, 2001 The problem of existence and uniqueness of continuous solutions of the following iterative functional equation \[ G\bigl[ f^{n_0} (x), \dots,f^{n_k}(x) \bigr]= F(x),\;x\in[a,b],\tag{1} \] where \(G\) and \(F\) are known functions and \(f\) denotes the \(n\)th iteration of \(f\), is investigated.
Zeqing Liu, Shin Min Kang
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Existence and uniqueness of neutral functional differential equations with sequential fractional operators. [PDF]
PLoS ONEIn this research paper, we investigate the existence and uniqueness of solutions for neutral functional differential equations with sequential fractional orders, specifically involving the [Formula: see text]-Caputo operator.
Rabah Debbar +4 more
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Generalizations of F. E. Browder's sharpened form of the schauder fixed point theorem [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1987 AbstractLet E be a Hausdorff topological vector space, let K be a nonempty compact convex subset of E and let f, g: K → 2E be upper semicontinuous such that for each x ∈ K, f(x) and g(x) are nonempty compact convex. Let Ω ⊂ 2E be convex and contain all sets of the form x − f(x), y − x + g(x) − f(x), for x, y ∈ K.
Kok-Keong Tan
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A generalization of the Schauder fixed point theorem via multivalued contractions [PDF]
, 2001 Summary: We establish a fixed point theorem for a continuous function \(f:X\to E\), where \(E\) is a Banach space and \(X\subseteq E\). Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.
Paolo Cubiotti, Beatrice Di Bella
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On extremal fixed points in Schauder's theorem with applications to differential equations
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2004 The author derives necessary and sufficient conditions for the existence of a least and a greatest fixed point of an operator which satisfies the hypothesis of Schauder's fixed point theorem. The main result is the following Theorem. Let \(N\) be an ordered normed space, \(D\subset N\) a non-empty, bounded, closed and convex subset and \(T\colon D ...
José Angel Cid
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Existence of Positive Solution for the Eighth-Order Boundary Value Problem Using Classical Version of Leray–Schauder Alternative Fixed Point Theorem [PDF]
Axioms, 2019 Thenmozhi Shanmugam, Stojan Radenovic
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The Schauder fixed-point theorem for connectivity maps [PDF]
Colloquium Mathematicum, 1981 Jack Girolo
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A new generalization of the Schauder fixed point theorem
Mathematische Annalen, 1967 Felix E Browder
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