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1.
Francisco J. Aragón Artacho 《Set-Valued Analysis》2007,15(3):307-315
Borwein’s norm duality theorem establishes the equality between the outer (inner) norm of a sublinear mapping and the inner
(outer) norm of its adjoint mappings. In this note we provide an extended version of this theorem with a new and self-contained
proof relying only on the Hahn-Banach theorem. We also give examples showing that the assumptions of the theorem cannot be
relaxed.
This author is supported by Grant BES-2003-0188 from FPI Program of MEC (Spain). 相似文献
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本文对J.-P.Aubin与H.Frankowska最近关于自反严格凸Banach空间中闭凸集值映射最小选择连续的于个结果加以讨论,首先在比自反性较强的一类空间中讨论了在弱ubin与H.Frankowska的条件下闭凸集值映射最小选择的连续性,其次对J.P.Aubin与H.Frankowska的结果给出了一个新的简单证明,最后用反例说明本文给出的条件J.P.Aubin与H.Frankowsaka条 相似文献
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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
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Asrifa Sultana 《Numerical Functional Analysis & Optimization》2017,38(8):1060-1068
In this paper, we obtain an existence theorem for fixed points of contractive set-valued mappings on a metric space endowed with a graph. This theorem unifies and extends several fixed point theorems for mappings on metric spaces and for mappings on metric spaces endowed with a graph. As an application, we obtain a theorem on the convergence of successive approximations for some linear operators on an arbitrary Banach space. This result yields the well-known Kelisky–Rivlin theorem on iterates of the Bernstein operators on C[0,1]. 相似文献
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Sheng-jie Li Wen-yan Zhang 《应用数学学报(英文版)》2007,23(1):141-148
In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in this paper is a generalization of the corresponding result in [3]. 相似文献
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完备凸度量空间中(次)相容和集值广义非扩张映象的公共不动点定理 总被引:5,自引:0,他引:5
本文在完备凸度量空间中,利用集值和单值映象(次)相容的一些条件,建立了数值广义非扩张映象存在公共不动点的一个充要条件和一个充分条件.我们的结果改进、扩充和发展了文[2~7]中的主要结果. 相似文献
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On Ekeland's Variational Principle for Set-Valued Mappings 总被引:1,自引:0,他引:1
Sheng-jie Li Wen-yan Zhang College of Mathematics Science Chongqing University Chongqing China 《应用数学学报(英文版)》2007,(1)
In this paper,we derive a general vector Ekeland variational principle for set-valued mappings,which has a closed relation to εk~O-efficient points of set-valued optimization problems.The main result presentedin this paper is a generalization of the corresponding result in[3]. 相似文献
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Bai Zhongzhi 《数学研究与评论》1998,(4)
1.IntroductionForapositivenumber1p∞andacomplexmatrixA=(aij)∈Cn×n,wedenoteby|A|p=ni,j=1|aij|p1pthelpnormofthematrixA,andbyA... 相似文献
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Tudor Zamfirescu 《Set-Valued Analysis》2000,8(3):295-297
We introduce the notion of a starshaped set-valued function, and relate it to convex set-valued functions. We prove a theorem which, in the convex case, implies that single-valuedness is exceptional if the function is not everywhere single-valued. A second result shows a remarkable costantness of images for starshaped set-valued functions. Both theorems were inspired from a result of Deutsch and Singer, which they strengthen. 相似文献
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在一致凸并具有一致G可微范数的Banach空间中,研究一类渐近非扩张映象迭代序列的收敛性,给出强收敛定理. 相似文献
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Boualem Alleche 《Numerical Functional Analysis & Optimization》2017,38(2):139-159
In this article, we develop results on the behavior of fixed points sets of set-valued pseudo-contraction mappings. Then, we investigate the notions related to the Aubin property and make use of connections between the two involved set-valued nonnecessarily Lipschitzian mappings to obtain results on the inverse of their sum similar to those in the literature generalizing Lyusternik and Graves theorems. By proximal convergence, we apply our results to the sensitivity analysis of variational inclusions. 相似文献
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In this paper, the authors introduce a definition of the Schwarzian derivative of any locally univalent harmonic mapping defined on a simply connected domain in the complex plane. Using the new definition, the authors prove that any harmonic mapping f which maps the unit disk onto a convex domain has Schwarzian norm ■≤ 6. Furthermore, any locally univalent harmonic mapping f which maps the unit disk onto an arbitrary regular n-gon has Schwarzian norm■. 相似文献
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本文着重研究了在什么条件下集值映射I λT的值域是全空间Rn这一问题,其中I是恒等映射,λ>0是任意给定的常数,T是一个极大η-单调的集值映射.文中主要结果部分地解决了C.-H.Lee,Q.H.Ansari和J.-C.Yao在2000年提出的一个公开问题.此外,针对真下半连续泛函的η-次微分映射,也讨论了上述问题. 相似文献
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This note established equivalence relations among the matrix norms related to the lp norm and the lp operator norm for 1≤p≤∞ , which completes the comparison results in [2]. 相似文献
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集值映射下的向量均衡问题解的存在性 总被引:3,自引:0,他引:3
程永红 《应用泛函分析学报》2001,3(3):285-288
利用广义的截口定理,本讨论集值映射和变序下的向量均衡问题解的存在性。 相似文献
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