Academic literature on the topic 'Wolff–Denjoy-type theorems'

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Journal articles on the topic "Wolff–Denjoy-type theorems"

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Budzyńska, Monika, Tadeusz Kuczumow, and Simeon Reich. "Theorems of Denjoy–Wolff type." Annali di Matematica Pura ed Applicata 192, no. 4 (2011): 621–48. http://dx.doi.org/10.1007/s10231-011-0240-z.

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Nakazi, Takahiko. "Rouché type theorems and a theorem of Adamyan, Arov and Krein." MATHEMATICA SCANDINAVICA 97, no. 1 (2005): 154. http://dx.doi.org/10.7146/math.scand.a-14969.

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We show Rouché type theorems using a theorem of Adamyan, Arov and Krein. As applications, we obtain a certain characterization of self-maps of the unit disc in terms of the location of the Denjoy-Wolf point and we study a function in the Smirnov class whose real part is positive.
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GAUBERT, STÉPHANE, and GUILLAUME VIGERAL. "A maximin characterisation of the escape rate of non-expansive mappings in metrically convex spaces." Mathematical Proceedings of the Cambridge Philosophical Society 152, no. 2 (2011): 341–63. http://dx.doi.org/10.1017/s0305004111000673.

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AbstractWe establish a maximin characterisation of the linear escape rate of the orbits of a non-expansive mapping on a complete (hemi-)metric space, under a mild form of Busemann's non-positive curvature condition (we require a distinguished family of geodesics with a common origin to satisfy a convexity inequality). This characterisation, which involves horofunctions, generalises the Collatz–Wielandt characterisation of the spectral radius of a non-negative matrix. It yields as corollaries a theorem of Kohlberg and Neyman (1981), concerning non-expansive maps in Banach spaces, a variant of a
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Huczek, Aleksandra, and Andrzej Wiśnicki. "On the Karlsson–Nussbaum conjecture for resolvents of nonexpansive mappings." Annales Fennici Mathematici 48, no. 1 (2023): 153–61. http://dx.doi.org/10.54330/afm.126009.

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Let \(D\subset \mathbb{R}^{n}\) be a bounded convex domain and \(F\colon D\rightarrow D\) a 1-Lipschitz mapping with respect to the Hilbert metric \(d\) on \(D\) satisfying condition \(d(sx+(1-s)y,sz+(1-s)w)\leq \max \{d(x,z),d(y,w)\}\). We show that if \(F\) does not have fixed points, then the convex hull of the accumulation points (in the norm topology) of the family \(\{R_{\lambda}\}_{\lambda >0}\) of resolvents of \(F\) is a subset of \(\partial D\). As aconsequence, we show a Wolff-Denjoy type theorem for resolvents of nonexpansive mappings acting on an ellipsoid \(D\).
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Huczek, Aleksandra, and Andrzej Wiśnicki. "Theorems of Wolff–Denjoy type for semigroups of nonexpansive mappings in geodesic spaces." Mathematische Nachrichten, May 20, 2023. http://dx.doi.org/10.1002/mana.202100404.

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Dissertations / Theses on the topic "Wolff–Denjoy-type theorems"

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Maitra, Anwoy. "On the Kobayashi geometry of domains." Thesis, 2019. https://etd.iisc.ac.in/handle/2005/4670.

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In this thesis we study questions broadly related to the Kobayashi (pseudo)distance and (pseudo)metric on domains in ℂn. Specifically, we study the following subjects: Estimates for holomorphic images of subsets in convex domains: Consider the following problem: given domains Ω1 ⊊ ℂn and Ω2 ⊊ ℂm, and points a ∊ Ω1 and b ∊ Ω2, find an explicit lower bound for dist(f(Ω1(r)), Ω2c) in terms of r, where Ω1(r) := {z ∊ Ω1 | dist(z, Ω1c) ≥ r} and f : Ω1 → Ω2 is any holomorphic map such that f(a) = b. This is motivated by the classical Schwarz lemma (i.e., Ω1 = Ω2 = ⅅ) which gives dist(f(sⅅ), ⅅc) ≥ 4
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Book chapters on the topic "Wolff–Denjoy-type theorems"

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Heins, Maurice. "A Theorem of Wolff-Denjoy Type." In Complex Analysis. Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9158-5_7.

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