共查询到20条相似文献,搜索用时 15 毫秒
1.
We continue to investigate cases when the Repovš–Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images. 相似文献
2.
本文对于取值在Banach空间的几乎下半连续映射引入两个相关的下半连续闭凸集值映射,得到集值映射的连续选择存在性的若干特征,从而将 Deutsch E,和Kenderov P,De Blast F.S.和 Myjak J,Przeslawski K.和 Rybinski L E,Gutev V.等人以及作者自己的关于连续选择存在性的结果作为推论给出.并用这些结论讨论了在开映射定理不成立的。情况下从Banach空间到赋范空间上线性连续算子的齐性右逆存在问题. 相似文献
3.
Maxim V. Balashov 《Journal of Mathematical Analysis and Applications》2010,371(1):113-537
We consider a definition of a weakly convex set which is a generalization of the notion of a weakly convex set in the sense of Vial and a proximally smooth set in the sense of Clarke, from the case of the Hilbert space to a class of Banach spaces with the modulus of convexity of the second order. Using the new definition of the weakly convex set with the given modulus of nonconvexity we prove a new retraction theorem and we obtain new results about continuity of the intersection of two continuous set-valued mappings (one of which has nonconvex images) and new affirmative solutions of the splitting problem for selections. We also investigate relationship between the new definition and the definition of a proximally smooth set and a smooth set. 相似文献
4.
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
5.
Dušan Repovš Pavel V. Semenov 《Journal of Mathematical Analysis and Applications》2007,334(1):646-655
Let and be any convex-valued lower semicontinuous mappings and let be any linear surjection. The splitting problem is the problem of representation of any continuous selection f of the composite mapping L(F1;F2) in the form f=L(f1;f2), where f1 and f2 are some continuous selections of F1 and F2, respectively. We prove that the splitting problem always admits an approximate solution with fi being an ε-selection (Theorem 2.1). We also propose a special case of finding exact splittings, whose occurrence is stable with respect to continuous variations of the data (Theorem 3.1) and we show that, in general, exact splittings do not exist even for the finite-dimensional range. 相似文献
6.
We give a characterization of set-valued mappings from a topological (measure) space into the class of real non-empty intervals admitting a continuous (measurable) selection. As an application we obtain a characterization of set-valued functions defined on IR n admitting an approximately continuous or an approximately continuous and almost everywhere continuous selection. 相似文献
7.
We begin by a short survey of various attempts in selection theory to avoid the closedness assumption for values of multivalued mappings. We collect special cases when Michael's Gδ-problem admits an affirmative solution and we prove some unified theorems of such type. We also show that in general this problem has a negative solution. In comparison with a recent result of Filippov, we work directly in the Hilbert cube rather than in the space of all probabilistic measures endowed with different topologies. 相似文献
8.
Let A+B be the pointwise (Minkowski) sum of two convex subsets A and B of a Banach space. Is it true that every continuous mapping h:X→A+B splits into a sum h=f+g of continuous mappings f:X→A and g:X→B? We study this question within a wider framework of splitting techniques of continuous selections. Existence of splittings is guaranteed by hereditary invertibility of linear surjections between Banach spaces. Some affirmative and negative results on such invertibility with respect to an appropriate class of convex compacta are presented. As a corollary, a positive answer to the above question is obtained for strictly convex finite-dimensional precompact spaces. 相似文献
9.
Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities 总被引:3,自引:0,他引:3
The variational inequality problem with set-valued mappings is very useful in economics and nonsmooth optimization. In this paper, we study the existence of solutions and the formulation of solution methods for vector variational inequalities (VVI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence of a solution of the VVI. It is shown that the optimization problem formulated by using gap functions can be transformed into a semi-infinite programming problem. We investigate also the existence of a solution for the generalized VVI with a set-valued mapping by virtue of the existence of a solution of the VVI with a single-valued function and a continuous selection theorem. 相似文献
10.
Francisco J. Aragón Artacho Michel H. Geoffroy 《Journal of Mathematical Analysis and Applications》2007,335(1):168-183
We study stability properties of a proximal point algorithm for solving the inclusion 0∈T(x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of our algorithm is uniform, in the sense that it is stable under small perturbations whenever the set-valued mapping T is metrically regular at a given solution. We present also an inexact proximal point method for strongly metrically subregular mappings and show that it is super-linearly convergent to a solution to the inclusion 0∈T(x). 相似文献
11.
Completeness, Sections and Selections 总被引:1,自引:0,他引:1
Valentin Gutev 《Set-Valued Analysis》2007,15(3):275-295
In this paper, we develop a general approach to set-valued semi-continuous selections which is based on order-like arguments
rather than on classical approximations. The approach works nice in a number of situations demonstrating the genesis of such
selection properties of set-valued mappings. In particular, it allows to generalize several known results, also to get some
new results about sections of set-valued mappings.
相似文献
12.
《Optimization》2012,61(3):263-276
In this note we introduce a notion of the weak contingent generalized gradient for set-valued mappings associated with the contingent epiderivative of set-valued mappings introduced in "E. Bednarczuk and W. Song (1998). Contingent epiderivative and its applications to set-valued optimization. Control and Cybernetics, 27, 376-386; G.Y. Chen and J. Jahn (1998). Optimally conditions for set-valued optimization problems. Mathematical Methods of Operations Research, 48, 187-200." and prove that, under some additional condition, it coincides with the weak subdifferential introduced in "T. Tanino (1992). Conjugate duality in vector optimization. Journal of Mathematical Analysis and Applications, 167, 84-97." when the set-valued map is cone-convex. We also study the weak contingent generalized gradient of a sum of two set-valued mappings and optimality conditions for a set-valued vector optimization problem. 相似文献
13.
In [HOLá, Ľ.—HOLY, D.: Pointwise convergence of quasicontinuous mappings and Baire spaces, Rocky Mountain J. Math.] a complete answer is given, for a Baire space X, to the question of when the pointwise limit of a sequence of real-valued quasicontinuous functions defined on X is quasicontinuous. In [HOLá, Ľ.—HOLY, D.: Minimal USCO maps, densely continuous forms and upper semicontinuous functions, Rocky Mountain J. Math. 39 (2009), 545–562], a characterization of minimal USCO maps by quasicontinuous and subcontinuous selections is proved. Continuing
these results, we study closed and compact subsets of the space of quasicontinuous functions and minimal USCO maps equipped
with the topology of pointwise convergence. We also study conditions under which the closure of the graph of a set-valued
mapping which is the pointwise limit of a net of set-valued mappings, is a minimal USCO map. 相似文献
14.
Jacek Jachymski 《Journal of Fixed Point Theory and Applications》2009,5(1):47-61
We revisit a fixed point theorem for contractions established by Felix Browder in 1968. We show that many definitions of contractive
mappings which appeared in the literature after 1968 turn out to be equivalent formulations or even particular cases of Browder’s
definition. We also discuss the problem of the existence of approximate fixed points of continuous mappings; in particular,
we settle it in the affirmative for Browder contractions. Finally, we recall three problems concerning Browder contractions
which remain unsolved.
With great respect for Professor Felix E. Browder 相似文献
15.
The purpose of this paper is to study a strong convergence of multi-step iterative scheme to a common solution for a finite family of uniformly continuous ?-strongly accretive operator equations in an arbitrary Banach space. As a consequence, the strong convergence theorem for the multi-step iterative sequence to a common fixed point for finite family of ?-strongly pseudocontractive mappings is also obtained. The results presented in this paper thus improve and extend the corresponding results of Inchan [6], Kang [8] and [9] and many others. 相似文献
16.
Jamal Rezaei ROSHAN Nabiollah SHOBKOLAEI Shaban SEDGHI Vahid PARVANEH Stojan RADENOVIĆ 《数学物理学报(B辑英文版)》2014
In [Aghajani A, Abbas M, Roshan JR. Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces. Filomat, 2013, in press], using the concepts of G-metric and b-metric Aghajani et al. defined a new type of metric which is called generalized b-metric or Gb-metric. In this paper, we prove a common fixed point theorem for three mappings in Gb-metric space which is not continuous. An example is presented to verify the effectiveness and applicability of our main result. 相似文献
17.
A. L. Brown 《Set-Valued Analysis》1997,5(3):195-208
Previous investigations of, in particular, continuous selections have led to the definition of the derived mappings and, here, the order of a set-valued mapping between topological spaces. The relation between the topological spaces and the possible orders of set-valued mappings between them is considered and examples are constructed to show that each ordinal number is the order of some set-valued mapping. 相似文献
18.
An-hua Wan Jun-yi Fu Wei-hua Mao 《应用数学学报(英文版)》2006,22(1):21-26
A new generalized vector equilibrium problem involving set-valued mappings and the proper quasi concavity of set-valued mappings in topological vector spaces are introduced; its existence theorems and the convexity of the solution sets are established. 相似文献
19.
Valentin G. Gutev 《Set-Valued Analysis》1998,6(2):149-170
The paper is devoted to selection theorems for continuous set-valued mappings which are not necessarily convex-valued on finite-dimensional subsets of the domain. As a result, we get natural generalizations of the famous Kuratowski–Dugundji extension theorem. The technique, developed in the paper, applies to l.s.c. mappings with paracompact, or similar, domain as well. Also, it leads us to a new construction of set-valued continuous selections that involves dimension-type arguments. 相似文献
20.
We study M-separability as well as some other combinatorial versions of separability. In particular, we show that the set-theoretic hypothesis b=d implies that the class of selectively separable spaces is not closed under finite products, even for the spaces of continuous functions with the topology of pointwise convergence. We also show that there exists no maximal M-separable countable space in the model of Frankiewicz, Shelah, and Zbierski in which all closed P-subspaces of ω* admit an uncountable family of nonempty open mutually disjoint subsets. This answers several questions of Bella, Bonanzinga, Matveev, and Tkachuk. 相似文献