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1.
In this work, we will prove the Dugundji extension theorem for the cone metric space. It is heavily reliant on the paracompactness of the cone topology that is proved by Ayse Sönmez in the paper Sönmez (2010) [11]. 相似文献
2.
杨大春 《中国科学A辑(英文版)》2003,46(5)
This paper introduces the fractional Sobolev spaces on spaces of homogeneous type,includingmetric spaces and fractals. These Sobolev spaces include the well-known Hajfasz-Sobolev spaces as specialmodels.The author establishes varions chaaracterizations of(sharp)maximal functions for these spaces.Asapplications,the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces.Moreover;some embedding theorems are also given. 相似文献
3.
Using the Borwein–Preiss variational principle and in terms of the proximal coderivative, we provide a new type of sufficient conditions for the Hölder metric subregularity and Hölder error bounds in a class of smooth Banach spaces. As an application, new characterizations for the tilt stability of Hölder minimizers are established. 相似文献
4.
This paper introduces the fractional Sobolev spaces on spaces of homogeneous type, including metric spaces and fractals. These
Sobolev spaces include the well-known Hajłasz-Sobolev spaces as special models. The author establishes various characterizations
of (sharp) maximal functions for these spaces. As applications, the author identifies the fractional Sobolev spaces with some
Lipscitz-type spaces. Moreover, some embedding theorems are also given. 相似文献
5.
Bas Lemmens Brian Lins Roger Nussbaum Marten Wortel 《Journal d'Analyse Mathématique》2018,134(2):671-718
We study the dynamics of fixed point free mappings on the interior of a normal, closed cone in a Banach space that are nonexpansive with respect to Hilbert’s metric or Thompson’s metric. We establish several Denjoy-Wolff type theorems which confirm conjectures by Karlsson and Nussbaum for an important class of nonexpansive mappings. We also extend and put into a broader perspective results by Gaubert and Vigeral concerning the linear escape rate of such nonexpansive mappings. 相似文献
6.
M. A. Prokhorovich 《Mathematical Notes》2007,82(1-2):88-95
Let (X, μ, d) be a space of homogeneous type, where d and p are a metric and a measure, respectively, related to each other by the doubling condition with γ > 0. Let W α p (X) be generalized Sobolev classes, let Capα p (where p > 1 and 0 < α ≤ 1) be the corresponding capacity, and let dimH be the Hausdorff dimension. We show that the capacity Capα p is related to the Hausdorff dimension; we also prove that, for each function u ∈ W α/p (X), p > 1, 0 < a < γ/p, there exists a set E ? X such that dim H (E) ≤ γ - αp, the limit $$\mathop {\lim }\limits_{r \to + 0} \frac{1}{{\mu (B(x,r))}}\int_{B(x,r)} {u d\mu = u * (x)} $$ exists for each x ∈ X\E, and moreover $$\mathop {\lim }\limits_{r \to + 0} \frac{1}{{\mu (B(x,r))}}\int_{B(x,r)} {\left| {u - u * (x)} \right|^q d\mu = 0, \frac{1}{q} = \frac{1}{p} - \frac{\alpha }{\gamma }.} $$ . 相似文献
7.
In this paper, we introduce some new function spaces of Sobolev type on metric measure spaces. These new function spaces are defined by variants of Poincaré inequalities associated with generalized approximations of the identity, and they generalize the classical Sobolev spaces on Euclidean spaces. We then obtain two characterizations of these new Sobolev spaces including the characterization in terms of a variant of local sharp maximal functions associated with generalized approximations of the identity. For the well-known Hajłasz–Sobolev spaces on metric measure spaces, we also establish some new characterizations related to generalized approximations of the identity. Finally, we clarify the relations between the Sobolev-type spaces introduced in this paper and the Hajłasz–Sobolev spaces on metric measure spaces. 相似文献
8.
We give a proof for the Hölder continuity of functions in the parabolic De Giorgi classes in metric measure spaces. We assume the measure to be doubling, to support a weak (1, p)-Poincaré inequality and to satisfy the annular decay property. 相似文献
9.
Slobodan Radojević Ljiljana Paunović Stojan Radenović 《Applied Mathematics Letters》2011,24(4):553-558
The purpose of the present paper is to establish coincidence point theorem for two mappings and fixed point theorem for one mapping in abstract metric space which satisfy contractive conditions of Hardy–Rogers type. Our results generalize fixed point theorems of Nemytzki [V.V. Nemytzki, Fixed point method in analysis, Uspekhi Mat. Nauk 1 (1936) 141–174], Edelstein [M. Edelstein, On fixed and periodic point under contractive mappings, J. Lond. Math. Soc. 37 (1962) 74–79] and Huang, Zhang [L.G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2) (2007) 1468–1476] from abstract metric spaces to symmetric spaces (Theorem 2.1) and to metric spaces (Theorem 2.4, Corollary 2.6, Corollary 2.7, Corollary 2.8). Two examples are given to illustrate the usability of our results. 相似文献
10.
Various Meir–Keeler-type conditions for mappings acting in abstract metric spaces are presented and their connections are discussed. Results about associated symmetric spaces, obtained in [S. Radenovi?, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (2011), 38–50] are used to show that the regularity condition for the underlying cone can be dropped in some fixed point results that have appeared recently. 相似文献
11.
A classical theorem of Euclidean geometry asserts that any noncollinear set of points in the plane determines at least distinct lines. Chen and Chvátal conjectured a generalization of this result to arbitrary finite metric spaces, with a particular definition of lines in a metric space. We prove it for metric spaces induced by connected distance-hereditary graphs—a graph is called distance-hereditary if the distance between two vertices and in any connected induced subgraph of is equal to the distance between and in . 相似文献
12.
In this paper, we study smooth metric measure space (M, g, e ?f dv) satisfying a weighted Poincaré inequality and establish a rigidity theorem for such a space under a suitable Bakry–Émery curvature lower bound. We also consider the space of f-harmonic functions with finite energy and prove a structure theorem. 相似文献
13.
Özlem Acar Vasile Berinde Ishak Altun 《Journal of Fixed Point Theory and Applications》2012,12(1-2):247-259
In the present paper we prove some fixed point theorems for ?iri?-type strong almost contractions on partial metric spaces. We also give an illustrative example. 相似文献
14.
15.
Wasfi Shatanawi 《Chaos, solitons, and fractals》2012,45(4):520-526
Samet and Vetro [Samet B, Vetro C. Berinde mappings in orbitally complete metric spaces. Chaos Solitons Fract 2011;44:1075–9.] studied a fixed point theorem for a self-mapping satisfying a general contractive condition of integral type in orbitally complete metric spaces. In this paper, we introduce the notion of a generalized ψ-weak contraction mapping and establish some results in orbitally complete metric spaces. Our results generalize several well-known comparable results in the literature. As an application of our results we deduce the result of Samet and Vetro. Some examples are given to illustrate the useability of our results. 相似文献
16.
Mathematical Notes - 相似文献
17.
The purpose of this paper is to develop the understanding of modulus and the Poincaré inequality, as defined on metric measure spaces. Various definitions for modulus and capacity are shown to coincide for general collections of metric measure spaces. Consequently, modulus is shown to be upper semi-continuous with respect to the limit of a sequence of curve families contained in a converging sequence of metric measure spaces. Moreover, several competing definitions for the Poincaré inequality are shown to coincide, if the underlying measure is doubling. One such characterization considers only continuous functions and their continuous upper gradients, and extends work of Heinonen and Koskela. Applications include showing that the p-Poincaré inequality (with a doubling measure), for p1, persists through to the limit of a sequence of converging pointed metric measure spaces — this extends results of Cheeger. A further application is the construction of new doubling measures in Euclidean space which admit a 1-Poincaré inequality.
Mathematics Subject Classification (2000):31C15, 46E35. 相似文献
18.
Sergey A. Timoshin 《Israel Journal of Mathematics》2010,179(1):211-234
We obtain a Wiener-type criterion for the Hölder continuity of extremal functions on general metric spaces in an abstract setting. Then we use this result to establish the boundary regularity of quasi-minimizers of the p-energy integral in the axiomatic framework of Gol’dshtein-Troyanov and also for extremal functions from the class of Poincaré-Sobolev functions. 相似文献
19.
Koji Fujiwara 《Mathematische Zeitschrift》2013,274(1-2):647-665
We discuss the Funk function $F(x,y)$ on a Teichmüller space with its Weil–Petersson metric $(\mathcal{T },d)$ introduced in Yamada (Convex bodies in Euclidean and Weil–Petersson geometries, 2011), which was originally studied for an open convex subset in a Euclidean space by Funk [cf. Papadopoulos and Troyanov (Math Proc Cambridge Philos Soc 147:419–437, 2009)]. $F(x,y)$ is an asymmetric distance and invariant by the action of the mapping class group. Unlike the original one, $F(x,y)$ is not always convex in $y$ with $x$ fixed (Corollary 2.11, Theorem 5.1). For each pseudo-Anosov mapping class $g$ and a point $x \in \mathcal{T }$ , there exists $E$ such that for all $n\not = 0$ , $ \log |n| -E \le F(x,g^n.x) \le \log |n|+E$ (Corollary 2.10), while $F(x,g^n.x)$ is bounded if $g$ is a Dehn twist (Proposition 2.13). The translation length is defined by $|g|_F=\inf _{x \in \mathcal{T }}F(x,g.x)$ for a map $g: \mathcal{T }\rightarrow \mathcal{T }$ . If $g$ is a pseudo-Anosov mapping class, there exists $Q$ such that for all $n \not = 0$ , $\log |n| -Q \le |g^n|_F \le \log |n| + Q.$ For sufficiently large $n$ , $|g^n|_F >0$ and the infimum is achieved. If $g$ is a Dehn twist, then $|g^n|_F=0$ for each $n$ (Theorem 2.16). Some geodesics in $(\mathcal{T },d)$ are geodesics in terms of $F$ as well. We find a decomposition of $\mathcal{T }$ by sets, each of which is foliated by those geodesics (Theorem 4.10). 相似文献
20.
《Journal de Mathématiques Pures et Appliquées》2003,82(8):975-1004
In this paper we give a natural definition of Banach space valued BV functions defined on complete metric spaces endowed with a doubling measure (for the sake of simplicity we will say doubling metric spaces) supporting a Poincaré inequality (see Definition 2.5 below). The definition is given starting from Lipschitz functions and taking closure with respect to a suitable convergence; more precisely, we define a total variation functional for every Lipschitz function; then we take the lower semicontinuous envelope with respect to the L1 topology and define the BV space as the domain of finiteness of the envelope. The main problem of this definition is the proof that the total variation of any BV function is a measure; the techniques used to prove this fact are typical of Γ-convergence and relaxation. In Section 4 we define the sets of finite perimeter, obtaining a Coarea formula and an Isoperimetric inequality. In the last section of this paper we also compare our definition of BV functions with some definitions already existing in particular classes of doubling metric spaces, such as Weighted spaces, Ahlfors-regular spaces and Carnot–Carathéodory spaces. 相似文献