共查询到20条相似文献,搜索用时 15 毫秒
1.
Yuri Brudnyi Pavel Shvartsman 《Transactions of the American Mathematical Society》2001,353(6):2487-2512
We prove that the trace of the space to an arbitrary closed subset is characterized by the following ``finiteness' property. A function belongs to the trace space if and only if the restriction to an arbitrary subset consisting of at most can be extended to a function such that
The constant is sharp.
The proof is based on a Lipschitz selection result which is interesting in its own right.
2.
Yuri Brudnyi Pavel Shvartsman 《Transactions of the American Mathematical Society》1998,350(4):1519-1553
The classical Whitney extension theorem describes the trace of the space of -jets generated by functions from to an arbitrary closed subset . It establishes existence of a bounded linear extension operator as well. In this paper we investigate a similar problem for the space of functions whose higher derivatives satisfy the Zygmund condition with majorant . The main result states that the vector function belongs to the corresponding trace space if the trace to every subset of cardinality , where , can be extended to a function and . The number generally speaking cannot be reduced. The Whitney theorem can be reformulated in this way as well, but with a two-pointed subset . The approach is based on the theory of local polynomial approximations and a result on Lipschitz selections of multivalued mappings.
3.
The purpose of this paper is to generalize and improve some topological properties of solutions set to the set-valued vector equilibrium problems by using the scalar characterization method. Moreover, the Lipschitz continuity of an approximate solution mapping for the parametric set-valued vector equilibrium problems is studied. 相似文献
4.
In this short note we give counterexamples to several results related to extension theorems published recently. 相似文献
5.
T. H. Sweetser III 《Journal of Optimization Theory and Applications》1977,23(4):549-562
A set-valued derivative for a function at a point is a set of linear transformations whichapproximates the function near the point. This is stated precisely, and it is shown that, in general, there is not a unique minimal set-valued derivative for functions in the family of closed convex sets of linear transformations. For Lipschitz functions, a construction is given for a specific set-valued derivative, which reduces to the usual derivative when the function is strongly differentiable, and which is shown to be the unique minimal set-valued derivative within a certain subfamily of the family of closed convex sets of linear transformations. It is shown that this constructed set may be larger than Clarke's and Pourciau's set-valued derivatives, but that no irregularity is introduced.The author would like to thank Professor H. Halkin for numerous discussions of the material contained here. 相似文献
6.
Generalized vector equilibrium problems with set-valued mappings 总被引:15,自引:0,他引:15
7.
Krzysztof Przes?awski 《Journal of Mathematical Analysis and Applications》2002,274(2):475-481
Stability of ε-optimal solutions for quasiconvex programs is studied. 相似文献
8.
9.
A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature. 相似文献
10.
11.
In this paper, we revisit the Mordukhovich subdifferential criterion for Lipschitz continuity of nonsmooth functions and the coderivative criterion for the Aubin/Lipschitz-like property of set-valued mappings in finite dimensions. The criteria are useful and beautiful results in modern variational analysis showing the state of the art of the field. As an application, we establish necessary and sufficient conditions for Lipschitz continuity of the minimal time function and the scalarization function, which play an important role in many aspects of nonsmooth analysis and optimization. 相似文献
12.
Maxim V. Balashov 《Journal of Mathematical Analysis and Applications》2009,355(1):277-537
We investigate when does the Repovš-Semenov splitting problem for selections have an affirmative solution for continuous set-valued mappings in finite-dimensional Banach spaces. We prove that this happens when images of set-valued mappings or even their graphs are P-sets (in the sense of Balashov) or strictly convex sets. We also consider an example which shows that there is no affirmative solution of this problem even in the simplest case in R3. We also obtain affirmative solution of the approximate splitting problem for Lipschitz continuous selections in the Hilbert space. 相似文献
13.
B. H. Pourciau 《Journal of Optimization Theory and Applications》1977,22(3):311-351
In this paper, four fundamental theorems for continuously differentiable mappings (the multiplier rule for equality constraints of Carathéodory, the inverse mapping theorem, the implicit mapping theorem, and the general multiplier rule for inequality and equality constraints of Mangasarian and Fromovitz) are shown to have natural extensions valid when the mappings are only Lipschitz continuous. Involved in these extensions is a compact, convex set of linear mappings called the generalized derivative, which can be assigned to any Lipschitz continuous mapping and point of its (open) domain and which reduces to the usual derivative whenever the mapping is continuously differentiable. After a brief calculus for this generalized derivative is presented in Part I, the connection between the ranks of the linear mappings in the generalized derivative and theinteriority of the given mapping is explored in Parts II and IV; this relationship is used in Parts III and IV to prove the extensions of the theorems mentioned above.This paper is lovingly dedicated to the author's wife, Nancy Arneson Pourciau.Each section of this paper has benefited from the consistently accurate advice and unflagging enthusiasm of the author's teacher, Professor Hubert Halkin. 相似文献
14.
LIAO Gongfu WANG Lidong & ZHANG Yucheng Institute of Mathematics Jilin University Changchun China Institute of Nonlinear Information Technology Dalian Nations University Dalian China Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2006,49(1):1-8
Consider the continuous map f : x → X and the continuous map f of K,(X) into itself induced by f, where X is a metric space and K(X) the space of all non-empty compact subsets of x endowed with the Hausdorff metric. According to the questions whether the chaoticity of f implies the chaoticity of f posed by Roman-Flores and when the chaoticity of f implies the chaoticity of f posed by Fedeli, we investigate the relations between f and f in the related dynamical properties such as transitivity, weakly mixing and mixing, etc. And by using the obtained results, we give the satisfied answers to Roman-Flores's question and Fedeli's question. 相似文献
15.
Roger J.-B. Wets 《Computational Optimization and Applications》2003,25(1-3):269-282
It is shown that local epi-sub-Lipschitz continuity of the function-valued mapping associated with a perturbed optimization problem yields the local Lipschitz continuity of the inf-projections (= marginal functions, = infimal functions). The use of the theorem is illustrated by considering perturbed nonlinear optimization problems with linear constraints. 相似文献
16.
In this paper,continuous homogeneous selections for the set-valued metric generalized inverses T of linear operators T in Banach spaces are investigated by means of the methods of geometry of Banach spaces.Necessary and sufficient conditions for bounded linear operators T to have continuous homogeneous selections for the set-valued metric generalized inverses T are given.The results are an answer to the problem posed by Nashed and Votruba. 相似文献
17.
In this paper, we continue our investigation of polyharmonic mappings in the complex plane. First, we establish two Landau type theorems. We also show a three circles type theorem and an area version of the Schwarz lemma. Finally, we study Lipschitz continuity of polyharmonic mappings with respect to the distance ratio metric. 相似文献
18.
We continue studying the class of weakly convex sets (in the sense of Vial). For points in a sufficiently small neighborhood of a closed weakly convex subset in Hubert space, we prove that the metric projection on this set exists and is unique. In other words, we show that the closed weakly convex sets have a Chebyshev layer. We prove that the metric projection of a point on a weakly convex set satisfies the Lipschitz condition with respect to a point and the Hölder condition with exponent 1/2 with respect to a set. We develop a method for constructing a continuous parametrization of a set-valued mapping with weakly convex images. We obtain an explicit estimate for the modulus of continuity of the parametrizing function. 相似文献
19.
DING Guanggui 《中国科学A辑(英文版)》2004,47(5)
In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of real l∞-type spaces, then we conclude that such mappings can be extended to the whole space as (real) linear isometries. 相似文献
20.
Zhong-bao Wang 《Applicable analysis》2013,92(3):616-635
Degree theory has been developed as a tool for checking the solution existence of nonlinear equations. Hu and Parageorgiou [S.C. Hu, N.S. Parageorgiou, Generalisation of Browders degree theory, Trans. Amer. Math. Soc. 347 (1995), pp. 233–259] generalized the results of Browder [F.E. Browder, Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc. 9 (1983), pp. 1–39] on the degree theory to mappings of the form f?+?T?+?G, where f is a bounded and demicotinuous mapping of class (S)+ from a bounded open set in a reflexive Banach space X into its dual X*, T is a maximal monotone mapping with 0?∈?T(0) from X into X*, and G is an u.s.c. compact set-valued mapping from X into X*. In this article we continue to generalize and extend the results of Browder on the degree theory to mappings of the form f?+?T?+?G. By enlarging the class of maximal monotone mappings and pseudo-monotone homotopies we obtain some new results of the degree theory for such mappings. As an application, an existence result of solutions for generalized mixed variational inequalities is given under some suitable conditions. 相似文献